Yes, considering the laws of the Forest comply to the laws of the state. In that, if the state allows carry in open areas, then the National Forest allows it. I've open carried several times in the Forests around NM and have had no problems with either the County Mounties who patrol under reciprocal agreements for the Forest Service, or the Forest Service LEOs and Rangers themselves.
AZ has similar laws to NM regarding open carry.
A bogus law to insure ones compliance.
Else re-education camp for you!!
You go in to a National Forest without a gun and you are a fool.