That's been my frustration on this thread too. Not only can you be armed in national forest, but they have (usually) open hunting seasons on these kinds of lands, and while carrying of rifles is restricted to hunting seasons, carrying a pistol for protection is not, any more than it is anywhere else, according to state law.
You are correct. Where I live, I am surrounded by National Forest with four National Parks nearby. I should have made it clearer that it is legal to carry a loaded handgun in a National Forest, as long as your state allows it.
Most people would be shocked to learn that it is perfectly legal to carry a loaded handgun in a National Forest in California (don't carry a rifle though, unless hunting it is season).