At the top of that waterfall is a seasonal pool right at the edge of the cliff. Great place to take a dip. Fantastic view out over Coalpits Wash.
Yes, I took that trail from the Chain Lakes plateau to Studhorse. Easy to follow. It's an old, un-maintained trail judging from an old map I have. It's not listed on current maps. The old trail then goes north from Studhorse to the main east-west trail between Grouse Lake and Wood Lake. It's easy, but a lot of growth and trees.
Going downstream Piute from Studhorse to confluence of West Fork is difficult. Lots of cracks and dropoffs and trail & error. I'm glad there's a direct route down from Chain Lakes. Thanks!