In the 1938 musical Knickerbocker Holiday this song is sung by an aging Peter Stuyvesant as a lament for his lost youth. So in context. In actuality, Kurt Weill and Maxwell Anderson wrote it to suit the limited range and gruff voice of their star, Walter Huston–probably why it was such a perfect fit for Willie Nelson, who recorded the song on his 1979 Stardust album of pop standards.
I’ve never thought of the song in terms of aging, though–incurable romantic that I am, I think of it in the context of a relationship that may or may not make it to December. Just sayin’– 😉