Sounds like quite the adventure. I suspect that there will be ample snow. Avalanche danger is considerable in the Sawatch right now - be careful!

Skinning Tigiwon Road right now is a great and long day out in its own right.
If you have aspirations for the mountain, plan on 2 days. Even on skis it can't be done in a single day right now. The snowpack back there in East Cross Creek is waist deep at minimum right now. Plus, the recent snow we've had in the last 3 days has been ample and wet.
Vail Mountain received 11 inches yesterday which means the HC Wilderness probably received an additional 3-6 on top of that.

Skin up to the Community House or beyond to the summer TH. That should be a good day.
Matt's right. Avy danger is sporadic right now.
Eagle County Avy Forecast