After having my horse suffocate horribly along my seemingly adequate minecart rail in Survival, I did some tests in Creative to see what exactly killed it.

I expected the ceiling was perhaps too low but apparently, even if the ceiling is as low as it can be on a minecart (which would usually suffocate me), the horse did not suffocate.
It did, however, suffocate from walls to the side of it, and testing further seems to suffocate only from blocks that are 1 block higher, then 1 block diagonally in the x or z axes as shown on the right hand side of screenshot which seems very weird and counter-intuitive and cost me a very awesome horse.

To reproduce:
1. Set up a rail & minecart with some open space to allow the horse to get on.
2. Set up blocks down the rail where you want to test the horse's suffocation range. (+1y, ±1x, ±1z, from the minecart on the rail)
3. Push a horse on the minecart, shove it down the track to the suffocation-blocks testing area, watch it suffocate whilst it seemingly has a plentiful oxygen supply.