No it doesn't, mounted combat would ruin the game. People will just hit and run everything all the time, be virtually invincible.
Other npc/monsters can ride horseback as well, such as a gang of bandits, and of course dragons will have no problem. Balancing the game isn't Tes's strongpoints and it certainty isn't what draws me into their games. If people stop complaining about game abuses and start expressing the distaste of the lack of content, then maybe we can levitate in future tes games. That's right, I went there.
Spell making, enchanting, alchemy, smithing...they allow the player to play with the game. Like it's a toy. I love sandboxes because it doesn't restrain the player and just let's them play the game there way. Thus, it's called a sandbox. But you can't just leave a kid in a sandbox and expect them to have fun. Toys that allow the kid to manipulate the sand and use their imagination is what makes it so intriguing, and it's no different to games.
We need more ways to craft our own, unique characters and adventures. If the game is too easy, then make more "unfair" challenges that forces the player to use intuition and be creative to overcome any obstacle. If you're using all you can, then the game is expected to be easy. And the game should react to this understanding that the player will and should "abuse" the power given to them. Here's an easy fix. If the player can fight on horses, so can the enemy. Higher level bandits should ride on horseback, chasing the player. If you have a high bounty, guards can pursue the player to submission. It's not that hard to come up with these things. It's just the work that goes behind it. My point is that there's so little to add in comparison as to how much it would add to the game. Using what is already in the game, they could give me exactly what I'm asking for. If they put in a little bit more, they can create a masterpiece.
Riding a horse and fighting:WASD/joystick tank controls for the left hand as usual, and the same first person fighting we always have had with the mouse/joystick in the right hand.
DONEAdding enemies that ride on horseback, that would probably have to be either in an expansion or in the next game.
As a mod? Sure, why not of course?
As official? No. Never.
Ever.
Are you that satisfied with the performance of horses in Skyrim that you would rather stay restricted from the option to fight back while riding one? Or perhaps the idea of mounted combat is repulsive to you?