Hola SalaChic,
According to the official website of the airport, there is an actual post office on the main floor of T4 at Barajas. You can see a map
here (and click on "Otros servicios" if it doesn't automatically come up).
I looked briefly at the T1 map, and it seems that there are mailboxes there on the first two floors. I didn't see anything for T3, but there is a also a mailbox in T2. Hope this helps!