Not sure if you can get to the upper levels around Cooper. There may still be snow on the road. You can check with the USFS office in Cle Elum at (509) 852-1100. There is plenty of camping at the intersection of the Cooper Lake road and the road to Salmon la Sac. The Cle Elum river campground is big and a few miles before the cutoff to Cooper Lake and has more amenities than the primitive sites at the intersection.
Cal this place half the time the Forest Service ask them what is open and what's not. They are in Cle Elum and out hiking about regularly.
Sahaptin Outfitters (509) 674-3938 http://www.sahaptinoutfitters.com