I expected that when a player was riding a horse and tries to go through a two block high space, they would not be able to.

When I went through a two block high space on a horse, my head went through the block.

Tame and saddle horse
Try to walk through two block high space
You're head will be in the block.
When you're head is in a solid block, you will see black. When it is in a transparent block like leaves or glowstone, you will have x-ray like vision.