Several courses here in Montana are on National Forest land. A few are leased ski resorts, but most are not. Each Forest is different in terms of their land management principles so some of these courses are more developed (baskets, tee pads, signage, etc...) than others (painted tree targets, tone poles, dirt tees, etc...). As someone who has a lot of first hand dealings with the Forest Service to help manage a few of these areas, all I can say is good luck. It is a time consuming and often very frustrating process dealing with a federal entity. It is best if there is an official club or group that the FS can officially recognize. The FS is broke, so more than likely all installation & maintainance, of the course and any infrastucture (like bathrooms, parking lots, etc...) will fall on said club/group.
We were lucky here in Missoula in that 2 of our courses on National Forest lands were established long before the FS knew anything about them. Therefore our Club was able to make improvements (baskets, tee pads, signs) to those courses in the name of "protecting the resource". The FS has made it clear to us that if those same courses were proposed today they would not be approved due to the environmental impacts.
Good luck and I wish you success!! Our National Forests are a national treasure and are great places for multiple use recreation! Convincing the FS of that is another matter...