While riding a horse, I hit the jump key (which I map to the z key in options). I appeared to dismount but the horse galloped in the direction we had been headed by itself.
As I was following it, I noticed my health bar was indicating I was talking damage although I couldn't see the source of the damage. Happened a few times. After about a minute, I was suddenly teleported into a cave where the horse was milling about and I was taking a suffocation damage although I couldn't see the source of the damage and was still moving about independently of the horse. Then I died.
The horse was wearing a saddle and iron armor.
I reloaded the save (for incidental reasons, I restarted Minecraft first) but I could not reproduce this issue. Jumping on a horse worked fine. I tried with and without the horse armor. The only time I could reproduce getting forcibly dismounted as by going in water. I had to build a bridge underneath the horse to regain control of it.