Used to be a ski tow at Mount Rainier NP near the Paradise Inn. Lou Whittaker was a long time concessionaire of the ski tow.
flbski is correct about BP & HR
BM/BW are apparently private land within the boundaries, according to the NPS fact sheet they are part of 2,010 acres of private institutional ownership
Couple of ski areas that border national parks include Ober Gatlinburg, Jackson Hole, Crystal Mountain.
Wintergreen VA borders an NPS unit.
Brian Head and Shawnee (PA) are super close to NPS units, I’m sure there are others. Mt. Tom VT did border an NPS unit but I think it closed prior.