Thanks for resurrecting this thread AFSC - I too wondered about the song, somehow never connecting the Nativity version with Irish. There are several versions of both song and tune I believe (there's a surprise). Loads of stuff on the Web, starting as usual with Wikipedia
http://en.wikipedia.org/wiki/The_Dawning_of_the_Day

I must say Linda sang it beautifully at the National Theatre. She was having trouble with her voice at that time, too. She's a great person, more power to her arm.