Need some quick advice. I've got a player obsessed with magic and hes seen a lot of critical role. They are currently level 4 and have almost no magic items in the party. 

From what I can tell there are no shops that sell magic items and hes gotten to the point where every new town he goes into every shopkeeper and is like magic items? No? Worthless! And throws up his hands. 

I tired to explain that there are items scattered around just they are powerful and rare. 

So the real question is how do you deal with a player like this and is throwing a magic shop into existence in this module game breaking? 

I haven't played or run RotFM, however:

(1) Common Magic Items are typically low impact, so a shop that has a few shouldn't be a big issue.

(2) More rare magic items can be very, very expensive. If your players never earn enough to afford magic items then making them available would have no impact on the game, (unless they tried to charm or rob the merchants). Though it could be frustrating for them to always be out of reach.

(3) Crafting magic items takes time. If a shop exists that makes custom order magic items, the players could interact with it, but probably wouldn't be able to see it through.

Players can be difficult and it is important to manage expectations early. Pre-made adventures operate with certain parameters, so a low-magic environment can be seen as a feature, rather than a problem. However, some people are always going to want things their way, and that's when you need to decide whether to draw a line, or compromise to make everyone happy.

It's good to recognize what motivates people, and it is also good to let them know that they need to earn those boons.

This is kind of a session 0 conversation where you set expectations about what level of magic there will be in the campaign. You could explain that they are in a pretty remote area and the people here have little use for magic items. 
One way is to tell him this isn’t critical role and this world works differently and magic items are, technically, optional. Or, as it seems you’ve tried, tell him to be patient and if he keeps complaining there will be no magic for anyone. Just say it with a smile.

Or, if you want to allow there to be a shop, you could do it with some slight of hand. Have there be items, but way more expensive than he can afford. Or If the guy wants to buy a +1 sword, let him buy it, then just remove it from the next treasure hoard where there is one.
I’d be careful though. Published adventures often calibrate encounters knowing what items the party is going to have, so giving them things early might unbalance an encounter or two. So you could remove it from the hoard and then have him buy it after. 

Officially, D&D suggests never having magic item shoppes at all ever. There are lots of good reasons for it. However, if the party were to find some common magic items and even some uncommon consumables like potions or scrolls, it should be okay as long as you don’t make it rain for them and charge appropriately. A common permanent magic item should be around 100-150 gold, uncommon consumables should be between 100-300 gold.

Your player might be looking for a Gilmore. And while he is as glorious as his goods, it would probably be better to not include one until the party is much higher level.

Is it possible that's just the player's choice of how to roleplay their character? Is it the player or the character who throws up their hands?

Both honestly, character is an aspiring mage and they hate that their cantrips dont keep up with other players melee weapons. Not only that I did do a session zero explain the Dale and the scenario soooo. Ill think about a low end shop and see what happens I think.

An aspiring mage might enjoy an Imbued Wood Focus.

Though, be warned that it works particularly well with Magic Missile as the spell technically only consists of one roll. It will do additional damage equal to the number of bolts.

Quote from Memnosyne >>

An aspiring mage might enjoy an Imbued Wood Focus.

Though, be warned that it works particularly well with Magic Missile as the spell technically only consists of one roll. It will do additional damage equal to the number of bolts.

 This is actually something not so game breaking he loves his fire and necrotic spells.. a wood associated with those would almost certainly go to helping him without breaking balance.

Honestly, I don’t think you need to change anything. I personally love low-magic settings and adventures. Your player just needs to have a little patience. (On which note, it’s intentional that cantrips are worse than weapon attacks, since casters get huge damage output from spell slots, which fighters don’t have. Trying to “fix” that will probably just upset the party’s warriors!)

That said, I have a list of magic items and prices based on Adventurers’ League rules: having a magic shop that sells only these consumables shouldn’t be a problem. I wouldn’t put one in every town, but Bryn Shander might have one, although the Forgotten Realms are much lower magic than Wildemount. Up to you.

Scrolls where Cantrip = 25 gp, 1st level = 75, 2nd level =150, 3rd level = 300.

Potions where Healing = 50 gp, Climbing = 75 gp, Animal Friendship, Greater Healing, or Water Breathing = 100 gp.

Bags of Holding and Driftglobes are also available for 400 gp each.

The shop should also sell acid, alchemist’s fire, holy water, components with a gp cost for spells up to 3rd level, and basic wizard gear like wands and daggers, all at the prices in the PHB. Make a list of the inventory and prices, and add a kooky old wizard shopkeeper, and your player should be pleased.

Hope that helps!

I wouldn’t change anything either.

Bluntly, the player isn’t playing his wizard very well if his wizard isn’t contributing more to combat than the martial PCs are at 4th level. Even playing a blaster with only 7 spell slots he can do an insane amount of damage with his leveled spells. Cantrips are something that Wizards use when they can’t cast a leveled spell. Throwing a couple of spells with durations like Grease and Dragon’s Breath into the mix and wizards shine!

Frankly, this was the first change I did for Rime. 5E feels ridiculously lackluster when it comes to magical rewards for players. I have never seen Critical Role but I know Taking20 said he uses a magic item shop in his campaigns. As do I. It's lame for players to get all this coin and nothing to spend it on.

"Because Critical Role does it" is probably the worst possible reason you could have for changing something about your setting, unless you are playing in the CR setting (Wildemount). ROTFM (which I keep mis-reading as RTFM, lol) is set in FR, not WM. Therefore, the player should be told not to expect the CR setting rules to apply to FR, and to ROTFM.

Unless you want to change it for your own reasons, a player should not be dictating the setting to you. If you don't want magic-item shops, don't have them.

I have had players ask me about this in my Roman Empire campaign. They haven't whined about magic item shops yet, because they were in a small outlying border town. Now they went to a port city, and they seem to have expected to buy things like +1 magic items there. Not happening.

Now, I did say, you can probably find almost anything in the city of Rome because, well, it's Rome in the Roman Empire. But anywhere else, nothing doing. Certainly not in a remote area.

Specifically for Rime of the Frostmaiden, look in Chapter 1. There is a section called "Magic in Ten-Towns" which gives advice on having common magic items available in SOME of the towns. See https://www.dndbeyond.com/sources/idrotf/ten-towns#MagicinTenTowns

Note that none of the towns are described as having any shops whatsoever, the published adventure just gives a single Inn and a single Tavern in each of the ten towns.

Quote from Morgoloth >>

Frankly, this was the first change I did for Rime. 5E feels ridiculously lackluster when it comes to magical rewards for players. I have never seen Critical Role but I know Taking20 said he uses a magic item shop in his campaigns. As do I. It's lame for players to get all this coin and nothing to spend it on.

 
On a related note, this is why 5e’s failure to implement a system for building your own castle (or wizard tower, or whatever) is a huge mistake.

In the beginning of the ten towns section there's a disclaimer you can share 

Magic in Ten-Towns

Characters hoping to procure powerful magic items or the services of a high-level spellcaster in Ten-Towns are out of luck. At best, they might be able to find common magic items for sale, or a friendly druid, priest, or mage who can cast spells on their behalf. For every hundred people in a town, there’s one such individual living among them.

Magic items and magical services available in Ten-Towns are summarized below. If an item or spell is not covered here, assume there is no friendly NPC who can sell or cast it.

Common magic items cost 100 gp each where they’re available, except for common potions (such as potions of healing), which can be had for 50 gp.

A friendly spellcaster will charge 25 gp for a 1st-level spell, 50 gp for one that uses a 2nd-level spell slot, or 150 gp for one that uses a 3rd-level spell slot, plus the cost of any expensive material components.

 (I see someone else already commented on this, sorry)

And we must note the language (with my emphasis added):

At best, they might be able to find common magic items for sale... Common magic items cost 100 gp each where they’re available

Which means that even common ones are going to be "rare" in this setting, at least regarding shops.

I would absolutely hold the line here, and not bow to the player's insistence that shops be made available to provide easy access to magic items. I would maybe even say, "Sorry, but I don't run D&D games on easy mode."

Wouldn't quite go that far. Just be honest and say that this setting is low magic, and you missed that blurb or forgot to mention it beforehand. It adds to the setting and theme of horror to make things more difficult. This isn't an "easy" campaign, and the lack of magic helps increase that difficulty. Apologize for not making that clear at the start and say that in the next campaign, if they want to play a higher magic setting, you guys can find one. If he still acts like a man-child after that, then he might be toxic and not worth including in your games. That happens sometimes. 

I think you can tweak existing rewards or add new ones to fit your party. But whenever you do that, ask yourself: could an artificer at my parties lvl infuse this kind of item? Also don‘t add to much extra, 1 extra item per character per every 5 lvl is more then enough. 

Let‘s take your wizard: at lvl 4 he may find a frozen tree branch that adds a +1 to fire damage rolls. Then around lvl 6 or 7 he may come across an NPC who can carve that tree branch into a wand of the war mage with a +1 to hit/DC and a +1 to fire damage for a commission of course. And later when your group ‚finds’ a ruby worth 1000 gold in a sunken ship around lvl 9, the same NPC can inlay it into the wand and allow your mage to store up to three spell lvls in his wand.

Rime of the Frost Maiden is set in the lonely, sparsely populated region of the far north known as Ice Wind Dale. Magic items are few and far between and this is just a characteristic of the setting.

If you are incorporating RotFM into your own campaign you are free to change it up however you like including adding magic item shops and thousands of magic items if you like. Of course with a huge region whose population has a few hundred to a few thousand people altogether spread over 10 towns, if there is a wide variety of magic items for sale then the folks of the ten towns might be rich with them if they can spare so many for sale. Many might choose to keep a +1 weapon in the family to defend themselves rather than sell it since money isn't likely to help you much unless all you want to do is buy passage out of Ice Wind Dale.

As DM, it is up to you how you want to build and design the world the characters adventure in, and up to you whether it makes sense or not. So, if it makes sense to you, have shops selling magic items wherever you like. However, in my opinion, unless you change the entire setting of Ice Wind Dale and the 10 towns, magic shops don't make that much sense since there isn't really enough population, money, or adventurers bringing them in to support it.

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However, on the topic of magic items and magic shops in general, I find that many of the more recently designed adventures go very light on magic items to the extent that it will make it very difficult for certain classes later on if the DM doesn't compensate for it.

Tomb of Annihilation has no magical bows and very few other magical weapons of any kind. It can easily run up to level 11 or more and without these, characters later in the game are at a significant disadvantage without such weapons. I played a ranged rogue through ToA and if I had not taken 3 levels of blade pact warlock (fey) with improved pact weapon, my character would have had serious problems effectively fighting many of the creatures late in the game.

WDH and DoMM appear to be similarly light on magic items. However, compare these to Curse of Strahd, Tales from the Yawning Portal and Ghosts of Saltmarsh for example there there far more magic items in old content transferred to 5e than in the more recent new content designed for 5e (I haven't looked at PotA, ToD, or OotA so I don't know how they compare).

Only Saltmarsh includes a magic item shop since the local representative of the Quartermasters of Iuz runs a brokerage, keeps aware of magic items that might become available for sale or trade over a large geographical area and can possibly use various means to complete sales and trades over long distances. However, this is part of the job of the organization since it is part of an intelligence gathering effort and they can skim the best items off the top and send them back to their homeland.

Anyway, magic item shops were commonplace in previous editions and less common in 5e due to limited attunement slots, bounded accuracy and a bit of a de-emphasis on magic items vs class development driving power at higher levels. (At least that is my take on it).

 I share Matt Colville's view on magic items. They are cool to have, to find and to use. I have never considered NOT including them in my campaign.

Considering that the main target customer for magic items are adventurers, I would put a shop that sells them in places like Waterdeep, Baldur's Gate, Suzail, Calimport, Halarahh. So places where adventurers actually visit and are welcomed. 

If you have magic items in your world then it's reasonable to assume that they are being sold somewhere. After all, adventurers who find those don't always need them - in fact, if the DM rolls for treasure then it's more likely that the item will be sold than used.

Now, let's talk about the nature of the shop - is it a specialized emporium where a proper enchanter sits and makes custom magic items? Or is it an all goods store whose owner buys interesting items whenever someone wants to sell them? Maybe a mix of both? A shop where someone makes items on demand would be fairly unrealistic - making a magic item is a long and costly endeavor so if that is the business model, I would expect high prices and long waiting lists. 

In my campaign you can buy probably up to uncommon items in those shops. Rare and very rare - you gotta travel far to places like City of Brass on another plane.