Am heading out there with 2 other guys to do the North Rim starting June 20. This is per the north rim trek planned out by Backpacker mag a couple years ago. IF you are interested, I have extra space with our permit since a couple of folks have bailed out. AM concerned about the snow as well. firstname.lastname@example.org
Anyway, some response I got from someone who did the trek last year:
I did this hike last September. The first leg of the trek can be difficult, as the trail is obscured by rock slides, and had lots of poison oak. We also found ourselves plowing through dense thickets of manzanita in steep loose dirt trying to find the trail. Be prepared to lose the trail, but if you keep heading north and west of where the rock slides are, you should find yourself on the old road at an overlook just opposite Bridalveil Falls.
Days two and three were longer than I'd expected, and there are some steady uphill stretches on those legs, but the entire hike was beautiful. The three campsites that Backpacker suggests you stay at are all very lovely. I expect there will be more people camping at the top of Yosemite Falls in June than there were in September, but who knows with all the snow in the Sierras this year?
Be sure you take the side trips to Eagle Peak and North Dome. Your final campground at the top of Snow Creek is spectacular. Camp on the exposed granite, and you'll find yourself face-to-face with Half Dome, looming larger than life, and enjoy watching it turn colors during sunrise and sunset. At night, we watched the headlamps of the climbers as they made their way up Half Dome's face.