Thanks for your reply!

The tag `access=private` is used some 16 million times in OSM, that's 350 times more common than `aeroway=aerodrome`.

Adding the tag `access=private` is supported in all the editors I know of, so I just went ahead and added it.

If you believe that maps should show private airports in a different way, I would recommend opening an issue at the corresponding renderer (e.g. for the default map it would be the openstreetmap-carto repository in github).

Cheers!