Greensleeves was a very popular folk song in England in the latter part of the 1500s. It was brought to America in 1616 by the Pilgrims and became well known in the U.S.A. as well.
The original lyrics of this song had nothing to do with Christmas or any other holiday.
If you cast me off so dis-cour-teous-ly
And I have loved you so very long
And delight-ing in your winning company
Greensleeves you were all my joy, and you know Greensleeves you were my delight-
Greensleeves, you're my heart of gold,
No one else but my dear LADY GREENSLEEVES.