A good idea in theory, good for some fun, and maybe worth a try if you feel up to it. In terms of use for Pvp, just know that there's a lot of reasons people don't do this already:
~Harder to see what you're hitting, move around, land hits, dodge, etc. Horses are faster, yes, but hard to control efficiently.
~If the server is lagging, it can literally be faster to just walk/run, since horses are a mob and thus slowed by lag.
~Lag aside, in some locations(like towns, or forests with either low hanging trees or a lot of trees) it is much more beneficial to be on foot, since horses are larger and require lots of open space to travel, and get stuck on leaves and rooves and such very easily.
~Most experienced Pvpers make use of potions when they fight, which would be quite awkward to do on horseback.
~Portals are an efficient way of getting to an enemy base fast to attack. Since horses can't go through portals, you'd either need to travel to your enemy's location every time you attack or waste apples to spawn a horse every time.
~I imagine skullsplitting would completely counter horse combat, since theoretically somebody could hit either the rider or the horse and both would take damage simutaneously. With this in mind, the horse is ultimately just giving the other person a larger target to hit.
Just my thoughts, but yeah, why I don't like minecraft horses >.>