Is a municipal airport treated like a normal public place which requires signage or registration with a no-carry list to ban firearms from being carried on the premises, or...
... is a municipal airport treated like a government facility such as a courthouse, post office, or DMV office?
Or is there some other rule regarding guns that are loaded, holstered or otherwise carried on or about a person?
Airport terminals designed primarily for part 121 airline operations which are actively screened by the Transportation Security Administration are beyond the scope of this question.
Laws vary from state-to-state, so if carry is not legal in those states, then this question is not being asked in regards to those states, obviously.