I never use a horse. I don't even use Shadowmare and wish it would stop mapping with me. If it dies, I could care less.
Until combat gets better so you can actually fight on a horse, they are pointless.
I feel the same way with Shadowmere. I don't want the damn thing following me around like a lost sheep, there are times when I want stealth which is hard with a horse clumping around behind you. I normally go into a bandit camp, let Shadowmere charge in and then walk away, he does die with several bandits hacking away at him but that's the only way to get rid of him.
Combat, herb gathering and so on should be possible while remaining on horseback.