Late this August, I did a mostly off trail high route along the Divide from Green River Lakes to Big Sandy. At that time it was almost snow free. Most of the perennial snowfields on the high alpine passes were greatly melted out and we navigated around them without crampons or axe. We crossed knife point glacier in trail runners and trekking poles.
First part of our trip was fairly dry–only two nights with light and intermittent rain. By the end of the trip Wx had settled into a pattern of violent late afternoon and evening T-storms, with driving winds, hail, sleet etc.
And the worst late summer blizzard I was ever in was in the Wind Rivers in September. We came over TX pass in driving snow and almost no visibility. So be prepared for just about anything in terms of weather.
Advice about checking with the Great Outdoors in Pinedale for local conditions (and a shuttle if needed) is good advice. The owner is a backpacker, has been in the area a long time, and is quite knowledgeable about Wx and backcountry conditions.
Have a good trip, -alan
