A PC wants to play as a Horse.

My birthday is coming up and I convinced my group of friends to play a one-shot with me. Some of them had sillier character concepts that they allowed me to create for them, and others went with more standard characters (like a elf Druid and tiefling rogue). One of these sillier characters is a human who only makes decisions by flipping a coin. I made them into a Trickery Cleric who's patron is Tymora. Easy. Another PC, however, wanted to play as a wizard... a wizard who is a horse.

I don't run a lot of homebrew in my games, so I started thinking about ways to go about this. Start the party at level 3 and give him 2 levels in Druid for wildshape? Early game polymorph item?

I eventually settled on making him a centaur using the Legacy/Expanded Rules race. His backstory is that both of his parents were centaurs, and he got the horse half of both. I thought this was a good way to make this character, but for those who are more educated than I am: Is there anything in the centaur stat block that may not fit a horse character?