Just to add:
I just got back from 6 days elk hunting in the Big Horn National Forest, Big Horn Mountains in Wyoming.
Not only was hunting allowed, but most of the NF Camp Grounds were open. The only exceptions were a few that are always closed in the winter. They are too hard to get snow removal equipment in.
Never talked to anyone who had problems. WY Game warden told me the NF, (in Wyoming anyway) don't seem to be effected by the shut down, although FS personal aren't working.
And before you ask, yes I got my elk.
CPT USAR Ret
USAMU Sniper School Oct '78
Distinguished Rifle Badge 1071