Bill,
Below are my observations on the Main Trail on 5/31. (Conditions: Perfect weather. The time when significant snow was encountered was between 6:30 AM and 2:30 PM. Then the snow was easy to walk on in trail running shoes. No significant ice or slush was encountered.)
(1) No significant snow until Trail Camp is reached.
(2) Possible to refill water bottle at Trail Camp.
(3) All snow from Trail Camp to the start of the Switchbacks.
(4) Approximately 85-90% of the switchbacks are free of snow.
(a) When a stretch of snow is encountered, usually following the footprints across it leads to where the trail resumes on the other side.
(b) Carefull attention to Risk Management (at least for me) currently is needed at the short Cable Section. (The Cables are down.) I used an ice axe to self- belay there.
(5) From Trail Crest to the back of Keeler Needle is essentially free of snow.
(6) From Keeler Needle snow is encountered for several hundred yards. The Summit is free of snow.
Those on the Summit Memorial Day were rewarded with a spectacular view of the High Sierras waking up from a long slumber.
However, for me another highlight of the day was on the decent. In the late afternoon I encountered Bob R coming up the trail near Mirror Lake. Was he beginning an adventure to some obscure location, our just out stretching his legs on a gorgeous afternoon in the Sierras? He was gracious enough to stop and answer some of my questions. In retrospect, I feel somewhat embarrassed. Bob was calm and composed, while I was probably babbling somewhat incoherently due to fatigue and being not well acclimated yet. Sorry Bob, if I was somewhat "out of it." But it was a long day at the Office!
Bill, have a great hike. Best wishes, Jim F