THIS IS A POST FOR XBOX 360 PLAYERS, SORRY IF I DISAPPOINTED YOU!
So anyway the main subject, Horse Combat.
This was a thing i didn't realize you could do when my friends said you could, since you couldn't do it on oblivion. It's actully quite easy, well for people with connection to Xbox live, so all you do is accept whatever download it throws at you when you go to play the game. Hopefully it'll be the 1.6 patch(it should be, because it's the latest patch released).
Now that You've hopefully downloaded the 1.6 patch, all you need to do now is obtain a horse, steel,buy,shadowmere or frost.
On to the weapons and moves you can perform whilst on horseback.
You can use any weapon apart from magic and shouts, when weilding a one handed weapon you can attack from both sides, to attack from the right side(the side your character will be weilding his weapon on) just press the RT button. To attack from the left press the LT button. It does take some good timing to pull of a good, useful attack. But when trying to do archery on horseback it's a different story. You need good timing and precision to get a kill, because when riding, the camera stick(the right analog stick) is for the direction of the horse, but you can change the aiming when still on the horse though, for it to be easier it's good to get eagle eye and steady aim. For me i use the two handed weapons when I'm not doing archery becuse they have better range and do more damage than one handed weapons, also you can do power attacks with swords,hammers and axes just the same way you would on foot, by holding down the button.
Thanks for reading and i hope i was useful to you.