Traveling on US 20 westbound, you approach the canyon from the south, driving over Eocene sedimentary rocks. Just before entering the canyon you cross the Owl Creek Mountains Thrust Fault. Rocks north of this fault (everything in the canyon) have been pushed up over the Eocene. This brings you suddenly into much older rocks, like the red-colored Chugwater Formation rocks from the Triassic Period, shown above.
Continuing north, you cross the Boyson Normal Fault. The fault itself is not visible in the photo below, but the layered rocks on the left (which are Mesozoic in age) lie south of the fault, while the more amorphous rocks on the right lie to the north. There is also a small reverse fault visible in the Mesozoic rocks.
Next up are huge thicknesses of Cambrian, Ordovician, and Mississippian sandstones, limestones, and dolomites. These rocks are generally strong and resistant to weathering, and form steep canyon walls up to several thousand feet high:
The Geologic Society of America has a Wind River Canyon Field Guide, by Edwin Maughan, which is available for download (pdf format).
Thermopolis is only a few hours south of our destination, and by late Friday afternoon we arrived at Shell Campground.