When Mail-art started is a difficult question. It all depends on how you want to see things. Best way to explain it is to cite the Wikipedia definition. You can read it all here:
Where it reads: An amorphous international mail art network, involving thousands of participants in over fifty countries, evolved between the 1950s and the 1990s It was influenced by other movements, including Dada and Fluxus.
It also explains a lot of different versions about the History....
Funny is that I started this entry in the Wikipedia on Mail-Art. Somebody told me that there was nothing there on the subject and I started to write for them. The current version is altered many times by many people, but it is funny to realize I started something there.