From what I can tell from reading the National Park website it is OK to carry as long as you are following the rules of the state that you are in. they give an example of Yellowstone being in three states and depending on where you are that state law applies. anyone know how that works in NJ, I hike regularly in in federal land and was wondering.
I believe it is OK so long as you do not enter any Federal structure - bears and gunowners sh*t in the woods 
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Yellowstone is a happy example, since Wyoming, Idaho, and Montana–the three states in which Yellowstone is located–all allow constitutional carry by nonresidents as long as they aren’t federally prohibited from owning a firearm. There are some small differences in prohibited places, but compared to NJ there are a lot fewer ways to get jammed up.