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
This is from a US Forest Service site:
"Rules on Firearms
What are the laws concerning carrying firearms on National Forest Land?
First, the primary laws governing possession of firearms and other weapons on National Forest are State Laws. These laws were developed by the states following establishment of our Cooperative Wildlife Management Agreements. Most notable of the state laws concerns controlling firearms on the National Forest are “cased gun laws”.
Cased Gun Laws: As the name implies, this law requires that all firearms on National Forest be unloaded and kept in a case. Virginia and West Virginia have similar “cased gun laws”. In order to allow hunting, these laws make an exception.
It is legal to have loaded firearms on National Forest during the authorized general firearms and muzzle loading gun seasons for bear, deer, grouse, pheasant, quail, rabbit, raccoon, squirrel, turkey, or waterfowl. This exception is very specific and applies only during the period when it is legal to take these listed species and doesn’t include carrying the loaded weapons in a vehicle.
Because hunting on Sunday is prohibited, carrying a loaded gun on National Forest is not legal on Sunday even if it is the Sunday in the middle of the general firearms deer season.
The second exception to this law allows people with a concealed weapon permit to carry a loaded, concealed, handgun either on their person or in their vehicle while on National Forest. This does not apply if the person is engaged in a primitive weapons season or chase only season.
Concealed handguns may be in the possession of hunters during the archery and muzzleloading seasons when they also possess a valid concealed handgun permit. Such handguns may not be used to shoot wild animals during these seasons.
Discharging a firearm, crossbow, or bow and arrow in or across a road or within the right-of-way of any road is prohibited by both State and Federal Law.
Any person convicted of a felony may not legally possess firearms on National Forest.