Christmas Day Ida Mornin' (and other spellings) is a Shetland "listening tune" from the repertoire of John Stickle of Unst; it was noted from him and subsequently published by Patrich Shuldham Shaw.  It is possible that it was written by John's ancestor, Friedemann Stickle, a renowned fiddler born in the late 18th century, who was paid to play it each Christmas morning at the house of the local laird.  Like most fiddle tunes, it doesn't appear ever to have been a song, though Tom Anderson reckoned that you could hear the title in the ending of the tune.

Having said that, Dick Gaughan's band Five Hand Reel set a text of The Knight and the Shepherd's Daughter to the first part of the tune back in the 1970s, which worked quite well.