I was up there on the 19-may doing PM-2.5 sampling; the trail to about 1/2 mile from Lower Pothole lake is fine then snow covered off and on to that lake; from Lower Pothole to Gilbert Lake again fine until about 1/4 mile to Gilbert where once again it is snow covered to the lake. Only went to Gilbert so can't tell you from there, but we can assume there is at least as much snow on the trail from there. Things are melting really fast up there right now.
On Saturday June 7, I went across Kearsarge Pass, down by Bullfrog Lake and on to the JMT. The ice is breaking up at Kearsarge Lakes significantly with the first lake mostly ice-free. Bullfrog Lake was ice-free as shown in the photos but there is still snow in the basin. It's melting fast and should not hinder your trip at all. Kearsarge Pass 6-7-08
Thanks JungleJim. I did a very long dayhike so no permit was required. I believe you would have to have a wilderness permit for any overnight trips into the area. Regarding wind, there was very little even at Kearsarge Pass. The only time I noticed any was on the descent from the Pass to Bullfrog and even then it was light.