You can carry whatever way the laws of the state you are in, allow, while you are in a National Park, in that state.
For example, here in WA you can carry (openly or concealed), without a recognized WA license or WA CPL, while doing a recreational activity like camping, hiking, hunting etc...therefore, in the National Parks in WA you can carry if it is legal for you to possess a firearm.
However, you cannot possess a LOADED long gun (Shotgun or Rifle) while in a vehicle,,,ever, so you would not be able to possess a loaded long gun in a vehicle while in a National Park either.
As for their "no guns" in their buildings...that is debatable...the law provides exemptions, they do not in their official statements. If you want to be the test case you can carry into their buildings and stick it to them, if you don't want the hassel of being cuffed and stuffed, and then fighting it in court...it would be best to stay out of building where NP personell normally work.