Hiking and mountain biking trails are in.
Water slides, tennis courts, and amusement parks are out.
Many of the U.S.'s ski areas are located on Forest Service land. While downhill and nordic skiing and snowsports are permitted in winter, there are further rules about what recreational activities are allowed on those Forest Service lands during the summer off-season.
All activities shall "encourage outdoor recreation and enjoyment of nature" (according to bill S. 607), thus hiking is in. So are ropes courses, zip lines, and frisbee golf.
I'll note that these are developed ski resorts we're talking about, not backcountry spots. Still, it's interesting to ponder the permits that allow certain outdoor business and their activities on public land.
You can learn more about the permits and the rules (or if you just like reading bills) in the following documents: