In "my" day (1967-1971) you were "supposed" to regsiter privately owned firearms with the MPs, I never did, don't know of anyone else who did. If you lived in the barracks you pretty much had to keep them in the arms room-or supply room in say a training unit with no weapons in its TO&E, if you lived in the BEQ or BOQ or family housing you kept them there.
Also in my day it seems "they" weren't so paranoid about weapons. The attitude was "You signed for it-you're responsible for it".