I don't like freezing cookies ever - I can always taste a bit of freezer in them. But people have different palates (and freezers!), and so I think this question is one of those things that's best for each person to test him/herself - particularly if selling, so s/he can vouch for the freshness/flavor of the product s/he is putting out. Best of luck!
(P.S. Also, any amount of condensation/water on an airbrushed cookie will cause that coloring to fuzz and/or bleed, so be very careful if you do freeze them.)