When playing in my survival world, I realized while riding a horse that it would occasionally get stuck while walking over one tall blocks. 

I tested this in a flat creative world and was able to recreate the effect. To be more precise, when a horse approaches one high block, it would start glitching out. It would remain in this state until the player changes the direction or if they jump. Getting off the horse has three noticeable effects; (1) the player gets off and the horse is fine (2) the player gets off and horse glitches to another side of one high block or through a hill and rebounds back. (3) Horse takes damage. I tried to test what causes the horse to take damage but the tests were inconclusive. The horse only occasionally receives damage when trying to dismount the horse while it is in its glitch state and would occasionally receive damage even after leaving the glitch state.

Further testing revealed that the horse gets glitched in all block variant that it can walk over. That includes stairs and other transparent blocks like glass.

As of currently, this is all I know about the bug. Thanks.