It took folks a few hundred years to decide they wanted to celebrate Jesus' birthday, and by then no one could remember which day it was. Looking around the calendar, they settled on December 25, a fortuitous choice because it was so near to the winter solstice, the birth of Sol Invictus, Saturnalia, and all the other big end of the year parties. I don't think Hanukkah was their minds because (from what I'm told) that didn't get big until much later, but I know that Sol Invictus was a big deal back then. Easing from him to Jesus was a masterstroke by Constantine.
And for those who prefer a saint to a savior (at least for this space), you won't do better than Fulk the Minstrel Bishop, an early thirteenth century Benedictine Cistercian. Hell, give him credit as a Dominican too, since he offered St. Dominic space, books, and one-sixth of the tithes in Toulouse to help him found an order of preachers. As a professional minstrel, Fulk seems like a good saint to share Christmas -- he probably could even remember all the words to "Good King Wenceslas."