+1 for what revor said about what to expect on wx.
You might consider reserving a camping cabin at the Lazy Acres Campground in Riverside (just south of Encampment).....they have showers! There is a cafe right across the street so you don't have to cook all your meals and next door is a nice little bar for liquid refreshments at the end of the day.
Lazy Acres Campground and Motel, Riverside, Wyoming
Get yourself a copy of the Medicine Bow National Forest Map and explore French Creek and Douglas Creeks along with your current plans. You won't be disappointed. You will be in bear country, get yourself a can of bear spray and you will most likely never see a bear, but at least you will be prepared in case it happens.