The American song - also known as The True Lovers' Farewell, Turtle Dove, Ten Thousand Miles and A-Roving On A Winter's Night, has its roots in a 17th century English broadside, in which it's a swan whose feathers will change from white to black. See Steve Gardham's article (scroll down and click on no. 20 in LH margin) for a discussion on the early history of this song.