I AM a military Freeper and the last base I was on definately required people who were living in the barracks to keep firearms in the armory. I wasn't living in family housing so I can't speak to that. This was in Texas in 2004.
Here is the Army Reg. Soldiers living in the barracks have to store personal firearms in their unit arms room. Soldiers living in family quarters must register them but can keep them in their quarters.
http://www.drum.army.mil/garrison/pw/pdf/Environmental/NatResources/FishAndWild/FD%20Reg%20190-6.pdf