Of course it depends on the type of cookie. I've successfully frozen chocolate chip, granola/monster, snickerdoodles, etc., both pre-baked (rolled in balls, frozen on sheets, then bagged; bake just before delivery) and already baked (cool for a couple of hours minimum, layer in bags with parchment or plastic between; thaw on cooling racks). The higher the moisture content of the cookie the better the texture after you thaw, but I've never really had a problem.
By the way, my preference is to bag the pre-portioned dough. I usually make 40 dozen cookies for my family Christmas party - the most I've ever done for one event, for myself or others - and I love that they are really fresh-baked.
For hand-iced cookies you can successfully freeze as well, but you have to be careful to let the icing dry for a couple of days before freezing (single layer in zip-top bags; thaw on cooling rack). The biggest challenge with these is spotting on dark colored icing; this is (I think) a result of the moisture leaving the cookie during the freeze/thaw process.