At least in the Army, most places stateside you can moonlight. It has to be approved by your local commander and not interfere with other duties (ie if you are on call and moonlighting at the same time, you would be expected to leave your moonlighting position to come see a soldier emergency if called).
Not that many moonlight regularly, because it's in addition to your regular 5 day work week. Those that do pick up an evening or weekend shift, or take a day of leave to work at an office.
The other thing that stops some people is state licenses. You can practice anywhere in the military as long as you have a state license somewhere, but if you are moonlighting, you will most likely need a license from the state you are practicing in.
Hope that helps.
