Before going off and firing in a National Forest, there are some "general" Federal regulations to understand for National Forests and BLM lands (NPs have their own restrictions):
You cannot shoot within 150 yards of a residence, building, campsite, developed area; across a road, trail or body of water; and no shooting into a cave.
Some may actually have some other regs due to protected areas; and not just due to game laws or protected species. One example is BLM wilderness study areas are prohibited in most BLM field areas and not due to animals; and they are not necessarily well posted but it is up to you to know. Some forests also have wilderness areas. So it is best to check with a ranger for that forest or field area.
In addition, be careful you don't shoot from Federal lands onto private lands. There are some forests around here (Utah) that are speckled with private and state lands surrounded by NF lands and the signs are not well posted, but it is up to you to know.
Other than those suggestions, national forest and BLM follow state laws on weapons and that means in at least one state (North Carolina) you cannot carry a concealed weapon into the National Forests (and maybe even the National Park...not sure about that) since it is written into state law you cannot carry into a National Forest (maybe even a National park too?).
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