I've been watching the snotels on both sides of the Winds. As of mid-March, snowpack was close to normal (90 percent or above). As of mid-April, the percentage was way way down, and stream runoff was higher than normal, indicating an early meltoff.
Here are a few places to check:
http://www.wcc.nrcs.usda.gov/snotel/Wyoming/wyoming.html (map of WY snotels; click the ones you want)
http://www.wrds.uwyo.edu/wrds/nrcs/snowprec/snowprec.html (snow water equivalent as percent of normal, listed by basin. For the Winds you want the Upper Green River and Wind River basins)
http://waterwatch.usgs.gov/?m=real&r=wy (stream flows--esp. Pine Cr. above Fremont Lake)
http://www.nohrsc.noaa.gov/nsa/ (snow depth analysis--click "Central Rockies" then "Snow Depth Analysis" There's quite a bit left at higher elevations, although not as much as last year. I suspect, therefore, that the early melting has occurred at lower or middle elevations (where the snotels are located). For a scary picture the other direction, look at Colorado--hardly any left.
http://www.pinedaleonline.com (Pinedale online news; often has links to photos from local hikers--one there now from a Memorial Day trip up the Sweetwater.
I second calling the Great Outdoors Shop in Pinedale; because they shuttle a lot of hikers, their info is probably more up to date than the Pinedale Ranger Station (Bridger-Teton NF). Actually, that's hard to tell because I always seemed to arrive in Pinedale on a weekend when the Ranger Station was closed. The visitor center at Elkhart Park, which is open weekends, knows nothing. The folks at Great Outdoors are great!
For the east side of the mountains (Popo Agie Wilderness), I got a lot of good help from the Lander Ranger station (Shoshone NF). NOLS should know, too, although they might not appreciate being listed as a contact for trail condition reports.
Stream fords, rather than really deep snow, might be your main problem.