Apparently if you know the right spots and how to access them, you can ride into July/August. However, I'm not sure that it would be all that great as you'd probably be dodging open water, difficult-to-pass rocks, sun-pocked snow, etc.
Regardless, it was a blast this weekend up there. The snow was such that you could really get good w/ techniques, climb long, super steep hills, nearly have to force yourself to get stuck and with the exception of some minor sluffing, the snow was pretty stable.