There is no prohibition, as far as I know, to carrying firearms on National Forest or BLM land if you have access to it. National Parks and National Monuments are another story and firearms are prohibited.
State lands vary with each state.
I have not looked up the laws specifically, but I live in a state, NM, where most of the recreation land is either Nat Forest or BLM. I have never seen anything that would prohibit carrying there.
That is one reason that I like the Feds owning most of the lands in the West. Where they don't the access is very limited or costs money, and you are at the mercy of the state or owner.
I'd recommend contacting the USFS Forest Supervisor or one of the Forest Service LEOs to make certain that their are'nt any local rules, regulations, or restrictions. While there may not be an agency wide restriction there may be local issues that apply only to that particular forest.
Just to be on the safe side, be sure that you are not on Tribal land. This is particularly important in the southwest, where it may not be very obvious, especially where tribal lands adjoin public lands. The tribal nations can have some very harsh rules about weapons and/or shooting on their lands.