Well, the second one is sung to the melody of a very famous German Christmas carol, named "Vom Himmel hoch" ("From Heaven Above"). I was so astounded when I heard it for the first time.
Later I researched a little and found out that the carol was written by Martin Luther (who was born not far from my city, btw) and used by Johann Sebastian Bach for his Christmas oratory.
So the melody they're singing is from the carol and the splendid wind section is by Bach, and I'm very, very fond of it.
Cheers!
Markus