It's pretty simple: Untamed horses can walk into and through blocks, even without being pushed. It only seems to happen to blocks of grass, and baby horses suffocate and die. I saw some horses spawn naturally in blocks, as well. It doesn't work with walls and only seems to work when it's a 1 high block.

What I expected to happen was for horses to not walk through the blocks randomly, and for the baby ones to not suffocate all the because of blocks next to it...

What actually happened was that horses and baby horses spawned in the ground, with the baby ones suffocating and dying. What also happened is that they can be pushed into one high grass blocks, as well as they can walk into them.

Steps to Reproduce:
1. Simply create a 3x3 ring of grass blocks
2. Spawn a horse inside the 3x3 ring
3. You can then nudge the horse in there, babies will suffocate