From the Wyo. G&F's FAQ page:
Q. Is it true nonresidents cannot hunt in national forest wilderness areas without a guide?
A. Basically, that's right. Wyoming statute says nonresidents must have a licensed guide or resident companion to hunt big or trophy game in national forest wilderness areas. The resident companion will need to get a free non-commercial guide license from a G&F office. The law does not prohibit nonresidents from hiking, fishing or hunting game birds or coyotes in wilderness areas. Only nonresident big and trophy game hunters must have a licensed guide or resident companion.
ODDNUT1
Kirt C.
Hunt Odds.com