Mooncruiser the only National Forests in the State of Arizona are the Coronado (Tucson), Tonto (Phoenix), Prescott N.F. (Prescott), Kaibab-Coconinno (Williams/Flag), Apache-Sitrgreaves (Heber / Springerville). The closure orders for the Tonto are listed on our website at:
http://www.fs.usda.gov/detail/tonto/news-events/?cid=STELPRDB5424729Each Forest posts separate orders but most are in coordinated to read similarly. The State (Arizona State Parks) and BLM are seperate as well and may or may not have different restrictions that would include Air Rifles.
I don't see any reference on the Tonto Order to airguns specifically, only to firearms. The news media routinely gets stuff like this wrong. I'm no expert but as I understand it an Airsoft gun is not considered a "Firearm" under State Law.
HOWEVER ... I would however assume that If any of our Forest Protection Officers (FPO's), or Game and Fish officer happens to see a bunch of people with what appear to be an AR's out rolling around in the woods he's probably going to assume you're shooting real steel and will take appropriate action to stop you. It may also be the case that other members of the public who are aware of the Fire restrictions are would see this activity and assume you're in violation which would not be good either.
So while it may be 100% legal it may not be the best idea. If an FPO wants to stop activity there are numerous Statutes that can apply, such as writing you a ticket for littering which I believe is around $500 for spreading plastic BB's on the ground bio or not. I know most of the G&F and USFS FPO's for the Tonto Area but the Prescott has shut down games before. Not sure about up North.
The bottom line is that I see postings for games in high country that are 1. unorganized and 2. near recreation areas. This is not a good idea as it would be extremely easy for the USFS to put a separate order banning all Airsoft and paintball rifles from their lands. If you are posting games on here that are happening on Federal lands make sure you aren't screwing it up for the Airsoft community as a whole.