Why would I want a horse?
Horses do the following:
- Allow for faster speed and have increased stamina for sprinting.
- Mounting a horse while over-encumbered allows for fast travel. (very useful)
- Can distract and attack enemies if provoked.
- Allows for climbing extremely steep slopes such as mountains.
- Will fast travel with you to places if lost.
As far as keeping a horse alive, it's hard, like you said. Shadowmere is a special horse with much more health and he respawns 15 days later if he dies.
I played the entire game without a horse. They're not required for any quests and aren't really worth the headache, in my opinion.
Edit: There's also the glitchy entertainment value.
They are great from getting to an objective point from the nearest avaliable fast travel.
Sometimes its a big trek, and when you fast travel to the nearest avaliable, it travels with you and spawns next to you. This allows an easy mounting, and then riding to the destination.
And lets be honest, you have lots of spare cash, and 1k every now and then isnt that much.
Another bonus to consider is that you can practically run up anything on a horse (within reason), where it would otherwise be too steep for your character. This in itself saves one heck of a lot time in certain scenarios. The amount of times I was thinking, I wish had bought another horse... Instead having to run right around to find the proper way up.
Update:
With the new expansion, it is now possible to fight upon your mount
Mounted combat is also included, which allows the Dragonborn to fight on horseback with a variety of weapons, but not spells
Download the "Better Horses" mod. It will make your horse experiences infinitely better. This really should have come with the game for anyone who wanted a horse, if for no other reason then because it makes horses cowardly instead of courageous. Although I'm sure you can still cast courage on your horse to make him fight!
The Headless Horseman is hard to keep up with on foot - a horse is useful for that. Also, it's useful if you lose your Shadowmere (mine Shadowmere died about a month ago and no sign of him since).