As stated previously, CENTCOM General Order Number One, in I believe the first paragraph, says no personally owned weapons in theater.
That being said, my wife is a Reservist, in Civil Affairs. She knows folks in the CA and Psyops community. One of her friends carried a Makarov, one that had been taken from a dead BG, around with him for most of his tour in Iraq. In addition to his M-16. There's a pic somewhere on this board of a Marine carrying a PPSh-41.
As far as weapons on base, CCW is not allowed, and if you're moving weapons around, they need to be unloaded and in the trunk. If you live in the barracks, they will stay in the arms room and be registered with the Provost Marshall (head MP), unless you arrange to store them off post somewhere. If your post has a POW range (most stateside posts do, with varying availability times-Ft Lewis was Fri-Sun, Ft Bennings was every day in spring and summer-going shooting at lunch was quite fun) you'll have to register your guns if you want to shoot there. Policy on weapons in post family housing varies by post-it wasn't allowed at Benning or Lewis, but Jackson allows it (registration required.)