I spent a week w/friends in GT and Yellowstone a couple years back in mid-late May. The weather was chilly; it snowed on our way out of GT up to Yellowstone. When we got to Yellowstone, one of the major north-south roads through the park was closed due to snow, though it opened during our stay. At higher elevations, there was easily a foot of snow on the ground, and berms from plows that were taller than I am ! Many shots have snow in them - other places had none. There was no snow on the ground in Jackson Hole while we were there, but we didn't have to hike up very high within GT Park to encounter snow-covered trails. On the plus side, the park was not very crowded, and wildlife was abundant ... in the span of a week, we saw & photographed plenty of bison (with calves), elk, caribou & mule deer; also bald eagles (two sightings) & osprey, moose (two sightings, both in GT), pronghorns, grizzly bear, black bear & cubs, coyote (2 sightings), marmot, beaver, a gray owl ... a friend who had been there in summer said that wildlife was nowhere near so easy to find on previous trips.