ooc: Sure, it's possible. Have a look at the
Ride skill and the
Mounted Combat sections for some of the things that are possible. If there's something you want to do that's not listed there, just describe it and as long as it's not ridiculously implausible, we'll work out a way to fit it into the rules. In the case of jumping the horse over the fallen tree... First, to control the mount in combat, you'll need a DC 20 ride check as a move action, since the horse isn't war-trained. Failure means you spend the rest of the round controlling the horse, and effectively can't act that round. Next, from the ride skill, the horse can jump obstacles as part of its movement, so you can make a jump check with the lower of your ride skill bonus (+5) or the horse's jump check bonus (+2 str -3 medium load = -1). The fallen tree we'll say is 4 feet high, so the vertical jump check DC would be 16. Failure would mean... various things, depending on how badly you fail.

After all that, William would still have a standard action left in which to attack. All in all, not great odds. If William wants to fight on horseback, he'd do well to buy a heavy warhorse, which would make this maneuver much easier. For this encounter, it's probably better to do as Octavio did, and attempt a DC 20 ride check to get off as a free action (failure means it takes a move action).