Quite possible... (i think)
I doupt horses can sidestep, so where your character would usually do that the horse turns... how you normally turn your charater (moving the mouse or using r3 on the ps3) would instead turn where your aiming... perhaps also the upper body... then you could swing your sword in any direction while riding in any direction... since you ride by kicking a horse with you feet (as far as I know) you could ride with a two hander, while dualwielding or using bow and arrow... if an enemy hits your horse and you don't have a free hand (having a bow would leave a free hand as long as you weren't loading or shooting with it) there should be a large chance that the horse would get scared and throw you off... the chance would depend on the damage inflicted to it... of course there'd also be a chance while you have a free hand (a hand you are holding on to the horse with) but it should be quite smaller... this would also leave some much needed reason to wield a onehander without anything else.
No offence, but you know nothing about horses
Horses can side step, look up the Lipizzaner horses, kinda just show stuff these days but a lot of what they do is old miltary training. Also if you are holding onto your horse with any hands at all, you are doin it so very wrong. Grip with the thighs, a well trained horse can even be steered with leg pressure leaving the hand totaly free.
Thats how the mongols conquered 1/2 of the world
game controls I could understand tho, Warband does it reasonably well but Skyrim seems to lack the open spaces for the mobility horse combat needs.
Pity you cant shoot from horseback tho, toggle auto run and free aim, (like gta etc)
the way it should be done --> http://www.youtube.com/watch?v=SKxvQsZGIhQ