Or you have amazing luck with horses...
My horses die every second or third battle I fight, which has caused me to dismount and heal them. I didn't use them prior to the horse combat patch at all, and I haven't started a mage character since that patch so I have no idea how they to keep them alive, but in Oblivion I always dismounted a long way away. It was annoying but it ensured they wouldn't join the fight.
For one, I employ jousting/cavalry type tactics when using my horse, I don't just stand next to the enemy and let them hit my horse 5 times in a row. I usually use a 2-hander to run in/out every few seconds, unleashing a power attack everytime I swoop in. It not only ensures victory, but the safety of my horse as well.
In RL, if you just stay in one spot with your horse while swinging at an enemy below you, you'll simply get yourself and your horse killed. It's no different in this game.
Honestly, I feel that I've perfected mounted combat. I would make instructional videos with tips on effectively using it, but I'm on 360. :/