Can someone tell me why or what the tradition is behind Indy winners drinking Milk?

Indy started during prohibition and in an attempt to mask any semblance of alcohol, the governing body decided they would use milk. Further, with the depression in full swing, this served as a way to promote American dairy products and show that milk was not just for kids. Little known is the fact the hooch was mixed in with the milk even at the first event and the winner was actually drinking a very White Russian. Even then, there was a Red Scare and so it was not actually known as a White Russian but instead a Herbert Hoover.

That's just my guess but I really have no idea.