National Forest is part of the Forest Service, not the National Park System. Controlled by the USDA I beleive. Their conditions for carry track along with state CCW laws in most instances. National Parks, forget it.
For Parks, the federal law is a prohibition for weapons, except for a few specific cases. Also, individual parks may allow it for certain areas, designated ranges, hunting, etc.
Weapon Regulations
Possession or use of firearms or other weapons in all National Park System (NPS) areas is prohibited (except as otherwise provided in the Code of Federal Regulations, Title 36 parts 7 (special regulations) and 13 (Alaska regulations). With rare exception (such as times when controlled hunting is allowed) weapons are to be dismantled completely and cased while visiting in NPS areas in the United States. In order to transport weapons through NPS areas they must be dismantled and adequately cased or packed in such a way as to prevent their use. Loaded weapons are subject to confiscation by park authorities.
Please contact the Chief Ranger or Superintendent of the park(s) you will be visiting for additional information concerning weapons, traps and nets.
Following is a reprint from the Code of Federal Regulations, Title 36 - Parks, Forests, and Public Property. It is Section 2.4 Weapons, Traps and Nets.
Code of Federal Regulations Title 36, Volume 1, Parts 1 to 199 [Revised as of July 1, 1998] From the U.S. Government Printing Office via GPO Access [CITE: 36CFR2.4] [Page 19-20] TITLE 36--PARKS, FORESTS, AND PUBLIC PROPERTY