Actually, in most versions of this song I've heard, it's a yellow ribbon. The green willow one is just the most famous as it was sung by Steeleye.

It was quite common for people to wear flowers & leaves around their hats in the C19th and earlier. I'd suppose the willow motif is symbolic of sadness - willows are traditionally associated with tears (and not just the weeping variety).

Cheers
IanC