It would also be "the snow".
The airport was closed because of snow (a general, widespread condition).
The airport was closed because of the snow (the specific snow in the specific area of the airport).
Both are correct for an airport, because it is large, but it is also a specific location.
We closed the window becauase of the snow. (Only the specific snow in the area of the window is of importance here, so we definitely use "the").
Bruce