Condition reports are hard to come by. The Inyo National Forest site posted this report last week (May 25th):
BACKCOUNTRY: Backpackers should be prepared with mountaineering gear for snowy/icy terrain, cold temperatures and sudden weather changes. Snow conditions make trails difficult to locate and passes very slick. Mountaineering and navigation skills are required. The snow level on the Whitney trail is approximately 10,000 feet (lower on north facing slopes). In Yosemite National Park, the current snow level is approximately 6,500 feet.
A hiker was up on Kearsarge Pass two weeks ago and posted these photos:
http://picasaweb.google.com/cunelson/Ke ... ssDayhike#
I had read that the road to the Onion Valley trailhead was closed, but this hiker's report clearly shows it is open -- cars are shown in the parking lot and one hiker slept overnight there.
Hey, if I were you, I'd give South Lake and Bishop Pass a try. If you find the conditions are just too difficult, there are plenty of other options at lower elevations to keep you entertained.
Have a blast!