Does the Moon have a postcade (or more likely, a zipcode)? Sounds like a stupid question, but I vaguely recall that on one of the Moon missions back in the early 70s, they took some envelopes or first day covers with them, and franked them there and brought them back to Earth. They must be incredibly valuable collectors' items by now. The zipcode system was in use well before that time, and for an item of post to be valid within the system, it would have needed to carry a zipcode. And, of course, I expect the Americans are anticipating the time when the Moon has a permanently populated base, and mail would become a daily regularity.
You're not thinking straight. The Moon, Madagascar, Mongolia or wherever don't have zipcodes, but they don't need one of their own to send mail to a zipcode address in the USA.
bert_h: If the US set up a base on the Moon, it would be US territory, much the same as Puerto Rico, The Marshall Islands or American Samoa, and all these places have US zipcodes. And perhaps what I should have said is that putting the zipcode on mail within the US - or its overseas territories - does facilitate the process. Mail without zipcodes arrives more slowly.