The GNF did their travel plan a couple years before fat bikes blew up, so nobody thought twice about a restriction on wheeled travel over snow. But most Nordic groomers do keep bikes off- same with our Nordic club.
Targhee actually has bike-only winter trails. The trails are too narrow and the turns are too tight for XC skis. It’s an awesome option when your weekend is booked in advance and one day of groomers is enough.