Anvils' hitboxes don't take up a full block on all 6 sides. This only happens on 4 of these. They're slightly less than a full block on the remaining two. When an anvil is placed on the ground, a horse can climb it. If the same anvil is placed on a block above the ground, a player can climb it by jumping one block at a time, but a horse cannot climb it without jumping two blocks.

This player will also likely experience glitchy movements, as if the player is trying to walk into the block, but is moved back to the hitbox boundary consistently.

I've seen bug reports on anvil hitboxes, but none that mentions horses, and the ones I can find seem to be resolved, even though the issue is still in the game.