So when taming new horses, or just on random occasions, horses are taking damage when saddles are removed, or when dismounting. At first, removing the saddle or dismounting did only 1-2 points of damage, but then with seemingly no change, the horse took 12 points of damage on dismount.
Horses are also getting stuck in a lot more blocks, and seem to frantically run back to the herds they spawned with even after they're tamed, at times.

( Another test done- on a horse with 11 hearts (22 health points), dismounting dealt 9 1/2 hearts (19 damage) to it, nearly killing it! Can't heal the horse when on it, so if it's dismounted again it'll probably die. :C )

UPDATE: I tested this myself in a creative server- I can't replicate horses taking damage when the saddle is removed, but they only seem to take damage on dismount after the horse has jumped or traversed up and down blocks. Sometimes it happens, sometimes it doesn't, looks like fall damage to me. 
In the picture below:
1) Horse getting stuck in blocks (front angle)
2) Horse getting stuck in blocks (back angle)
3) Horse taking damage on dismount after jumping (max bar) 5 times
4) The horse's health after taking damage (5 1/2 hearts or 11 damage points)