National Forrests are public property? I dunno bout in UT but as long as you dont cut trees without a permit, hunt at the correct season you can do whatever you want out there.
Avoiding danger is no safer in the long run than outright exposure. The fearful are caught as often as the bold. - Helen Keller.
"Hunting: Big game hunting has traditionally been the major wildlife attraction on the Forest, although recently there has been an increased interest in viewing and photographing all types of wildlife. Mule deer are harvested on every District, and elk are expanding their range on the Forest."
I don't know the National Forest you are near but it appears that within the state hunting seasons you can hunt in National Forests.
“Attitude is more important than the past, than education, than money, than circumstances, than what people do or say. It is more important than appearance, giftedness, or skill.”