Have fished out of Edwards, Co for the last 7 years August-September. You have the eagle river at the foot of beaver creek with plenty of public access.
In Glenwood Canyon or up above State Bridge both about 30 mins from Beaver Creek you have the Colorado River.
In Vail itself you have Gore Creek and 45 mins east of Beaver Creek you have the Blue River.
If you want to drive further afield you can do the Roaring Fork, Frying Pan or Yampa all about 90 mins from Beaver Creek
All in all you have a full range of waters to fish with plenty of public access - the decision is which ones not to fish.
Snow usually starts around mid Sept but no real heavy accumulations, normally. October is a great time to be throwing big streamers out there.