I suggest reviewing RCW 9A.20, 9A.36, and 9.41. When researching airsoft-pertinant State laws in Washington those were the sections I kept copies of.
It is my understanding that airsoft is prohibited on government or public land and within city limits. Airsoft should only be played on privately-owned land. Expressed written permission from the property owner(s) is required if the property owner(s) is/are not present.
Also, my friends and I got kicked out of a State park a few years ago for openly carrying airsoft guns with orange tips. According to the park ranger, BB guns, pellet guns, airsoft, paintball, dart guns, and other similar projectile launchers are prohibited from State parks. He did not include real-steel firearms on his list.
But if you're asking about National Forests, those would be covered by Federal Law, would they not? As such they should have the same laws in every state unless I'm mistaken.