[MENTION=93081]Davedamon[/MENTION]
Nice start! I have some specific critiques below. I actually ran a horse chase/combat with a similar feel - the degree they succeeded/failed on skill checks allowed them to move a number of relative squares (all speeds were 10, but I would have made lower speeds a equivalent penalty to the checks).
I like how you add speed damage to one of the obstacles, and that makes sense to use as a guideline for falling off your horse.
Some things can be game enders (stun, slow, immobilize, etc), and players love to stunlock enemies to foil a chase. On the one hand I'm inclined to let it play out and whatever happens happens. On the other hand it can totally kill the anticipation around a good chase. Like how you handle being unseated (prone), I really really like that.
I don't care for the "you always move your relative speed even if it takes you past where you want to be". Maybe it makes sense for an out of control wagon, but not for a skilled rider.
About difficult terrain, do you deal with it according to the number of (relative) squares moved, or is it like a "streaking" obstacle where it affects everyone as it "moves" through their space, thus relative speed? The second makes more sense to me.
How would you rule a charge? It's important for PCs with mounted combat feat on warhorses.
I notice that the horsemanship checks seem to use the PCs' own skills. Which is fine, but it's definitely ignoring/changing the rule that riders without Mounted Combat must use the mount's acrobatics, athletics, endurance, and stealth checks. IOW you're diminishing the value of the Mounted Combat feat (which may be fine for your purposes).
Despite those critiques, I really like what you've designed

It's very yoinkable, if you don't mind?