I was camped at shepards pass, at the base of Mt Tyndall (~12,000') on saturday night. When we got there, there was no snow. Up on Tyndall, we could see a little, but not much. While saturday was a beautiful day, it began snowing around 3:00 a.m. on Sunday. Not too much snow accumulated, I would guess only about an inch or two fell. It was very windy though, so we put off a summit attempt of Tyndall.
I would guess that at most, you would only encounter an two or or three inches above 12,000'. Even then, it may be bare in some places and drifted in others. Probably in the 20's at night though! Plan for winter conditions.