As a Kölner by birth that localism does ring a faint bell though I wouldn't have said it's a Cologne thing if you had pushed me on it. We do have plenty of localisms due to the historical proximity to France though, and it always amuses me that "Plümo" (duvet) for example is completely unheard of in most of the German-speaking world and is usually replaced with the far less graceful and to me frankly confusing "Oberbett".

But the general term, as a verb, is "Lüften" or specifically "Stoßlüften" for the shorter form that is often mandatory for apartments with modern insulation but lacking a proper vent system to prevent mold.

On a sidenote: an interesting folk etymology exists for the Rhineland word "Fisimatenten", meaning something like "shenanigans", deriving it from French "visite ma tente", literally "visit my tent": the claim is that mothers would advise their daughters to avoid "Fisimatenten" because French soldiers during the Napolean occupation might invite them (in French) into their tents for, well, shenanigans.