The eastern end of the Pasayten Wilderness could be somewhat melted out in a month, but hey, snow is not evil. Trying to cross a jagged ridge with 45-degree corniced slopes still covered in feet of snow is one thing, but a little postholing out in the gentle east end of the Pasayten is nothing to worry about, just an adventure. The east end out there is much drier than the more westerly stuff near the crest. The Horseshoe Basin area, for example, often melts out in May, but this year has more snow than usual. From there, there are lots of local peaks to hike/scramble, plus options to continue west along the Boundary Trail or check out Windy Peak to the south. It's a great area for just rambling off trail. Beware, though, much of the southern tier of the Pasayten Wilderness has burned in various fires in the last dozen years. Depending on your disposition and the intensity of the sun, making way through, e.g., the Lake Creek, Andrews Creek, or Chewuch valleys can be either demoralizing slog or high adventure. The northern tier is intact, and green. Here's what the Cathedral area (a little farther west from Horseshoe Basin, and likely to melt a little later) looked like this past weekend.
As mentioned above, great resources for ideas and conditions are:
The WTA hiking guide
nwhikers.net trip reports
WA snotel info
Also, NOAA has a snow pack prediction model (pick Snow Depth in the left-hand drop-down menu) that can be helpful, but should be taken as an interpretation. It's not always representative of reality, but does give a good rough idea of where things stand.