The law in NH is pretty simple: a license is required to carry a handgun that is both loaded and concealed, or to carry a loaded handgun in a motor vehicle (concealed or not). (You also can't carry any loaded long gun in a vehicle, period; that's a game & fish law.)
You can read everything here: http://www.gencourt.state.nh.us/rsa/...OC-XII-159.htm
RSA 159:4 addresses carrying concealed without a license. There is no law stating that open carry is legal; there is simply no law making it illegal. The only law requiring a license (RSA 159:4) specifies loaded, concealed handguns. Everything else is legal.