OK...
So I just tried with the newest snapshot... 16w07a
Horses still just stand there when you mount them during taming. you get bucked off and then they rear
in riding, the horses jump forward OK
But after you ride around for a while, and you dismount, they take damage
also, if you have ridden for a while and then remove the saddle, they also take damage
I tried again in the pre release and it's a tiny bit better but not really