It's been my experience in late May to find snow on the Mt Whitney trail, often from about the 11K' level, which is below Trail Camp. Snowshoes are usually not required as the snow has consolidated, but crampons often are, at least in the early/late hours, and it would be a good idea to have an ice axe. Whether the switchbacks will be open by then is a good question, but if not, climbing the snowfield below Trail Crest is not difficult. It's just a long, steep, slog. Typically there's less snow on the west side of Trail Crest due to its exposure, and a large snowfield often persists, sometimes into July/August not too far below the summit, but this snowfield is navigated easily.
