OK, so the problem is that there are 2 stables at opposite ends of the campground, and to make matters worse, they're both called Tri-Circle "D".
The stables where the horseback riding originates is at the Outpost. The main bus stop for Ft. Wilderness is in front of them. Across the street is the check-in building.
The other, at the Settlement, is where the draft horses for carriage rides and the MK horsecars are stabled. It's next to the pavilion for Mickey's Backyard BBQ and behind HDDR & Trails' End. There's a small bus stop shelter next to it, just down the road a piece from the Settlement bus stop. That's where I think MV's pick up for the Settlement.
It sounds like MV's can pick up at both the Settlement and the Outpost.