For the most part each seperate installation commander makes the rules for his installation.
Civilians carry weapons to fro from Ft Huachuca all the time. They can shoot at the post skeet/trap range and at the plinking range.
Most Army installations work the same way. Weapons are supposed to be registered with the Provost Office and they give you a certified print out that they are registered and if questioned at the gate you just show the print out.
No big deal.
Civilians are also allowed to hunt on Fort land.
I doubt there is any Federal law. Would be under Army, Air Force, Navy, whatever regulations.