I was driving through Hoback and Swan Valley last night so I got to put an eyeball on the river. The Snake river above the reservoir is muddy. The lake is starting to settle out and there is about 2-3 feet of visibility at the Dam. The South Fork looks somewhat clear coming out of the Dam with possibly a 12-18 inches of visibility, until Palisades Creek. At the Spring Creek Bridge the water is off color but you could fish with a large stonefly nymph, bright streamers and glo bugs. It appears that the runoff in starting to back off and the water from the tributaries should be clearing off in the next week or two. Once the tributaries clear up the river will become a aqua green color it will have a few feet of visibility and will start fishing really well. Dirty water will actually produce more fish on the fly with the water this color. Very similar to an overcast day, the fish will feel more protected which means they will eat more aggressively.
If I was going fishing today on the South Fork I would set up a nymph rod with a big bright streamer/leech type of pattern and a rubberleg as a dropper. I would also have a streamer rod set up with a sink tip and a big meaty fly. I would fish the upper section, Dam to Spring Creek.