I have a Florida CCW, along with Maine, Pennsylvania, Connecticut, New Hampshire, Utah and Virginia. I can (and do) carry in 35 states.
I have been stopped many times while carrying in different states (ok, I tend to drive a bit fast) and have never been asked. Some states require you inform the officer but most do not. Check packing.org for info on what states require you to tell the officer. Some states even have it noted when they call in your license information if you have a CCW for that state. (VA for example)
In any case it's no big deal. Keep your hands where they can see them and be polite. The fact that you have a CCW reassures most officers (in gun friendly states) that you have a clean record.