I was riding a horse in my base (who doesn't want to)and the horse auto jumped onto a crafting table pushing me into the celling of the only 3 block tall room. Saddly I suffocated and died, when I was taking damage the horse health bar was flashing but not going down which shows the horse was not being damaged. When I died the horse died too. I tested this in single player and only the player died. I would expect the horse not to die on realms if the player dies.