Is it the poor AI?
As a sneak archer, i hate how my horse charges into battle and will get in my line of sight, or give away my position. Anyone else dislike how eager horses are to engage in combat... and often die?
Is it the lackluster design or animations?
Skyrim is a beautiful game with great design elements. Horses, however, look ugly. They also move and behave unrealistically. Anyone who played RDD knows what I'm talking about. Rockstar's horses looked and behaved realistically (though they maneuvered too well at speed). I loved watching my RDD horse swat flies with his tail, graze when hungry, etc. Also, the forced 3rd person perspective is a poor design choice for players that want to stay in the 1st person perspective to enhance immersion.
Is it because Skyrim's horses aren't very useful?
Horses can't maneuver over certain rocky terrain and often get caught on a small rock. This limited mobility forces the player to stick to roads, which inhibits natural exploration. No mounted combat makes wilderness encounters a more tedious process, since you have to dismount to engage. Horses also have a tendency to wander off, and we can't whistle to call them back. It's also a hassle when traveling with companions, since they can't mount a horse or even sprint.
So with all of that, does anyone still use and like/love horses in Skyrim?
First of all, if your horse is getting in your way, then it is your own fault. I always hide my Horse in an area about a hundred yards away, before engaging in battle.
As for the animations, I play rpgs mostly for depth rather than fancy movements.
It is strange that you say horses perform poorly on rough terrain. I found it to be the exact opposite. I feel as if my character, by himself, cannot leave the road without having major impediments to his movement. When I get on a Horse, I can get the tops of mountains extremely fast.
I will agree that mounted combat should have been implemented. If any of you have ever played LoZ: Twilight Princess, then you undoubtedly know that mounted combat can be done very well.
I use horses for what they are desinged to do, and that is covering distances quickly. I have no major complaints, besides the lack of mounted combat.