Righto. It could be quite easily balanced by:
1. Making 'Horsemanship' it's own skill. If you want to get nasty at killing from the saddle, you have to put the time in - the skills you use on your feet won't be enough.
2. Making Horses vulnerable. This not only balances mounted combat, but makes Horse Armor actually valuable.
3. Making Horses expensive to purchase and maintain. This, combined with greater vulnerability, would make you think twice about every potential encounter. Also, horse thieves.
4. Horse Psychology. In addition to PC skill, make it so that individual horses have be trained to endure the stress of combat situations, otherwise they might spook and buck the rider at the first sign of trouble.
Perfect. Absolutely perfect.
@Everyone who's saying "it wouldn't fit the series": Are you blind? The fact that Tamriel has horses alone warrants horseback combat. Pretty much every real-world society that physically possessed horses used them for war. Tamriel is full of people wearing armor so heavy that it would only be used from horseback in real life (that's how medieval knights owned the opposition; charging in metal suits on the backs of war horses).
The human societies in Tamriel, Cyrodil especially, are built around the use of horses. There are fields to till, roads to travel, and peace to be kept across the continent. The lack of fighting from the saddle is forgivable the older titles, for obvious reasons, and in Morrowind, which seemed to lack horses as a society, and even Oblivion, being the first game on a new set of consoles. But that was 2006. The last title had very limited, even irritating use of horses. If you wanted to ride to your destination sans-fast travel, you had to stop and get off every two minutes or so to fight off some bandits, or a wolf, or a Minotaur. It was a supreme annoyance, especially with a slow dismounting animation. Logically, a bandit dumb enough to run down the road at a mounted swordsman would be cut down by the passing rider, or trampled, or both. There is no good reason for Bethesda to not have built the game around their use from the ground up, as sense would dictate they would after the half-assed Oblivion horse-riding.
Now, I've seen people on these forums passionately pine for billowing cloaks (to be fair, I want them too), prettier rain, more intricate clothing, and more realistic eating and drinking animations (seriously?), but this topic, one which directly addresses a glaring feature of the game (or lack thereof) that directly affects what the player can do in-game seems to have been neglected. When there are more threads about clothing than gameplay, there is a problem. If there are horses, why can we not use them as people in a pre-industrial society like Skyrim's would use horses? Why is what must be such a huge element of the game's world so neglected?