Service members shipping out for an overseas assignment receive a briefing that covers a lot, usually including possession of privately owned vehicles and weapons. If it doesn't, the briefing officer or NCO will be able to answer the question.
In general, no matter what anyone tells you what they or someone did in WWII, Korea, Vietnam, or the War of 1812, the U.S. armed forces generally ban privately owned weapons in combat zones and in most overseas areas. There are exceptions in some areas for hunting guns, but not handguns.
I strongly recommend you do NOT try to smuggle a gun into the area or have it shipped to you illegally. That kind of thing can lead to military prison, which, I am told, is no fun at all.
Jim