I dropped a card in the mail slot at the Poly on Wednesday. When I arrived home today I found the stamp I meant to put on the card. Do you think Disney put a stamp on it for me?
Yes, and the local post office picks it up directly, as the PP stated, which is the USPS (United States Postal Service). They wouldn't put a standard mailbox in the lobby of each resort, because it wouldn't match the overall decor, so the USPS agreed to a certain design that was acceptable to denote the mailbox, but not stand out like a sore thumb.
I hope you have your return address on it, so they can return it to you.
The other scenario is that they deliver it to the correct address with a "postage due" statement with it, so whoever received it will have to pay the $.44 cents. I've had this happen to me in the last year.