We are about to play this adventure and of course my son discovered Dragonborn on D&D Beyond and now wants to use that race.  This doesn't seem appropriate for the adventure since the entire thing revolves around fear of all things dragon related and slaying a Dragon at the end.  Has anyone done this? 

I would allow the player to play a dragonborn, nothing says they cant.

I would have the townsfolk be more cautious around them, especially if they are a white dragonborn but no mechanical changes. There are a lot of ways to incorporate it into the story, maybe they despise Cryovain because it is terrorising peaceful citizens or maybe they hate the dragon part of their lineage. There is a lot of RP potential from playing a dragonborn in DoIP.

Cryofang is a white dragon, a member of a relatively most bestial species.  It isn't Smaug or anything so sophisticated.  It can be played as a primative, uncaring menace.

I play a brass dragonborn (brass), paladin who's even more engaged in the mission due to his background.

I have a player playing a dragon born in my game. Depending on how you define the world Dragon born are not as exotic or rare as you think and most people know the difference between a Dragon Born and a real dragon. It is one of the standard races in the PHB 

But I did allow for an amusing roleplay moment, when the party went into the town ( I have expanded the NPC's of DOIP, and I removed the clunky Job Board and instead dotted the quests around the town with various NPC's). So the very first quest the party went to get, which happened to be from the mayor, who I turned into a Halfling, I had him barricaded in his house, scared of the dragon. The dragon born knocked on the door and the conversation went something like this. 

Mayor "Who is is, who are you, what do you want" 
Player "We heard you might have some work that needs doing, we are a handy group of adventureres just got into town" 
mayor "Are you really, your not the dragon are you, come to eat me" 
Player "No I am not a dragon come to eat you" 
Door opens a crack, dragon born smiles at mayor who screams and then needs ot be convinced that no this is not the dragon, for one thing the dragon is white and the dragon born is red. for another the Dragon is massive and the Dragon born is not (although to the halfling they seem pretty big). 

The benefits of having a dragon born, they can know a bit more about the dragon race (intelligence or history rolls to determine what they know when knowledge is important). SO for instance Cryovin in my game is already impacting the local environment, meaning that Spring seems to be taking longer to come, and even on a sunny day there is a cold chill in the air. The dragonborn rolled well enough to understand that Dragons affect the local environment so it will have wider issues in the future then just killing a few people. 

Also be aware that Dragonborn alignment and behaviour is not determined by there colouring, but depending on the society it is possible that Metallic dragonborn might look down on Chromatic's as being lesser then them simply because of there colouration. 

I have a gold dragonborn in my Dragon of icespire peak campaign. Why not? I made it so harbin wester is terrified of her with his dracophobia or whatever.

Just a quick update on this.  I allowed it and as everyone suggested, I just made the townspeople a little more wary of the group.  I even had them roll a charisma check anytime they spoke with someone to see if that person would react positively or not (aka run away).  The group caught on and started having the dragonborn player wait outside or keep his distance.  It was actually kind of fun and brought some more interesting moments into the game.

We are still working through the first three quests, but I'm confident this will work out fine and I'll find more ways to goof around with this.

Thanks for all the suggestions.