This situation occurred at the game table this past week. We were facing a mounted opponent and the Druid in the part cast Soften Earth & Stone to trap the opponent in deep mud. The DM rolled a reflex save for the mount, which subsequently failed and thus was "unable to move [or] attack" for one round.
A discussion subsequently ensued however about what the rider could or could not do. He had targets adjacent to him that he would normally be able to attack. It made sense to all of us that he personally wouldn't need to make a roll to avoid being stuck in the mud (he's on a horse after all). However, a horse doesn't really take up a full 10' square. It's an abstraction, designed to show how the horse needs that much room to manuver and wheel around in combat.
We ended up with a middle of the road solution, requiring a DC15 ride check (the same DC to use your mount as cover) in order for the rider to lean over and attack. Consequences of failure did not come up since he made the check. However, we're all curious as to what the community at large thinks. Should the rider be hindered at all by the mud? Should he be allowed to attack adjacent targets freely? Is the ride check a good solution, and if so is the DC appropriate and what should be the consequences for failure?
I like the solution. I would probably only let the rider attack to one side and likewise only let foes from that side attack him with melee weapons. Failure to make the roll I would let go as inability to reach except on a drastically poor roll, when I might ask for a confirmation check which, if he failed, might drop him in the mud, especially if he's riding bareback.