How to buff the dragon of icespire peak?

Quote from Sanvael >>

E.g. average character damage is 30 per turn if they hit with everything. 5 characters = 150 damage. Halve it to 75. I want the fight to last 3 turns, so 3 turns x75 hp = 225 hit points.

 Alternately, design your monster so after its action on turn one half the party is down; your math is assuming the PCs all get to attack every turn. In the end, the PCs are doing 75 damage per round and probably have something like 200 combined hit points (damage * hp = 15,000); a single monster's damage output doesn't go down as it takes damage so it can be around damage*hp 10,00 (that's based on hitting, so for raw numbers probably double it to 20,000).

A Young White Dragon has a raw dpr of about 90 in round 1 and 41 in subsequent rounds, so if we assume a two round encounter our total is 65*133=8645, which his less than half our target. I'd actually be a bit tempted by converting to a Mythic: when Cryovain is reduced to 0 hp, his hp reset to 133 and he gains new mechanics.

My players are 

. Drow evoker

. Very tanky half orc paladin

. Dragonborn paladin

. Half elf valor bard

. Human samurai 

The samurai can through 76 damage with Dragon slayer at cryovain in one turn. The dragonborn paladin can do 44 and the half orc 48.

Quote from RedKnuckles435 >>

The samurai can through 76 damage with Dragon slayer at cryovain in one turn. The dragonborn paladin can do 44 and the half orc 48.

 Expected damage includes the chance of missing. But yes, having a dragonslayer weapon does push damage above typical (also, if the PCs have prepped for cold resistance, you may need to push damage higher to compensate).

You can also give the dragon allies/minions. The encounter system doesn't handle mixed CR very well so it will look odd with DMG methods, but a generally good rule of thumb is that if you take two medium encounters (or two built via XGTE) and combine them, the result will be a quite hard fight. I suggest 8-12 ice mephits -- they're thematic, just having them cast their intrinsic Fog Cloud will seriously annoy the PCs (and aids the dragon by quite a bit, because it has blindsight), they can safely use their powers around the dragon and vice versa, and as long as they don't bunch up unless on top of the PCs, aren't that easy to just fireball away (particularly since sculpt spells only works on creatures you can see, so you can't avoid hitting the PCs).

I don't want a damage output too high, but lots of hp will hopefully wear down the party. Don't forget the stone cold reavers as well. They are a hard encounter.

I am also DM'ing DoIP for a party of 5 characters - human wizard, dwarf fighter, elf cleric, halfling rogue, and half-orc bard.  (Kind of vanilla, I know, but my players include my two young nephews and my young son who have never played before so we kept it pretty simple.  The half-orc is my adult niece.)  They're 3rd level now and just had a pretty easy time dispatching orcs at Butterskull Ranch and ankhegs at the Logger's Camp.  I'm using xp to advance their levels, but even if they do the side adventures (Shrine of Savras, Tower of Storms) I'm going to have a tough time getting them to 6th level on xp alone, before they face Cryovain at the end.  However, I'm starting to think maybe they don't have to be 6th level to face him/her (I guess the dragon's gender is up to the DM?).  Could five 5th-level characters reliably defeat Cryovain as written in the adventure after a tough fight, or would it be a toss-up with potential death of one or more characters?  (I'd hate for my nephews or son to lose their characters.)

Maybe give Cryovain kobold minions to amass treasure from the surrounding countryside and then guard it. Have a confrontation break out with the Reavers and the kobolds and they now ally with your party to take them down, unfortunately, also causing enough ruckus to wake Cryovain.

I personally like to use the lair actions as inspiration for dragons especially since fizban's game a bunch of optional ones.

• One such effect is a freezing fog this is very powerful on a white dragon because they are immune to cold, it obscures and they have blind sight. So why not give cryovane a freezing cloak that give disadvantage to attack him and damages anything that comes close.Alternatively his breath could leave behind an obscuring freezing cloud. 
• Another effect is forming ice walls maybe part way through the combat cryovane entombs himself in an ice sphere to heal or prepare spells
• another is heavy wind they could use an effect like warding wind or maybe you simply have heavy wind give disadvantage

Another thing I do is look at spells.

• Maybe this dragon has learnt to channel it's breath weapon into long range projectiles like the freezing sphere
• spike growth could be used as a lingering breath effect instead of the freezing cloud
• Maybe this dragon defends themselves with ice like  an armor of agathys 
• You could add the effect of rime's binding ice to it's breath

Another trick I sometimes use is special reactions 

• For dragons I like to say they can use a reaction to negate effects that would make sense for it's element.  So an ice dragon like cryovane could use it's reaction to shield itself with cold effectively  using [Tooltip Not Found]  on water spells and gaining resistance or negating fire spells. 

There's loads of options you should be able to create a unique and powerful dragon using those kinds of ideas. 

• You could have melee dragons that travels in a frozen cloud of ice and when threatened it seals itself in a ice cocoon and builds up an ice and applies an armor of agathys
• You could have a long range dragon hiding in heavy wind lobbing exploding ice balls at the party every round in the form of freezing sphere 
• You could have a dragon which uses it's breath to cover the ground in deadly ice spikes and then uses something like gust of wind to push the party into them 

That is incredibly thought out and I am definitely using these suggestions.