I usually end up killing my horse because it does those things. I'm an archer, so I'll be aiming and firing at an enemy and then my horse will charge in between us to trample the guy and take an arrow in the butt. The horse will then try to kill me, forcing me to finish it off. If I leave the fight to the horse, it will often die as well. So my horses are all suicidal apparently and don't know how to stay the hell out of a fight.
The first horse I had (I think from Whiterun? It's like one of the first horses you get) was pretty weak and died in a fight against wolves, but my second horse from Solitude actually seems pretty tough. He even took a whole bunch of damage when he aggro'd a dragon who had landed, and once I was able to lure the dragon away and kill it I thought the horse was dead, but he was still standing a few feet away. So I'm guessing Imperial horses = the bomb.
Also, horse vs dragon is insanely epic to watch.