Read "How December 25 Became Christmas" an excellent article in the recent addition of BAR (Biblical Archaeology Review) by Andrew McGowan.
The sum of the article is that the Christian tradition for a December 25 date predates the "pagan sun festival" that it is almost unanimously associated with the Christmas event. Here are a few excerpts.
The most loudly touted theory about the origins of the Christmas date(s) is that it was borrowed from pagan celebrations. The Romans had their mid-winter Saturnalia festival in late December; barbarian peoples of northern and western Europe kept holidays at similar times. To top it off, in 274 C.E., the Roman emperor Aurelian established a feast of the birth of Sol Invictus (the Unconquered Sun), on December 25. Christmas, the argument goes, is really a spin-off from these pagan solar festivals. According to this theory, early Christians deliberately chose these dates to encourage the spread of Christmas and Christianity throughout the Roman world: If Christmas looked like a pagan holiday, more pagans would be open to both the holiday and the God whose birth it celebrated.
Despite its popularity today, this theory of Christmas’s origins has its problems. It is not found in any ancient Christian writings, for one thing. Christian authors of the time do note a connection between the solstice and Jesus’ birth: The church father Ambrose (c. 339–397), for example, described Christ as the true sun, who outshone the fallen gods of the old order. But early Christian writers never hint at any recent calendrical engineering; they clearly don’t think the date was chosen by the church. Rather they see the coincidence as a providential sign, as natural proof that God had selected Jesus over the false pagan gods.
It’s not until the 12th century that we find the first suggestion that Jesus’ birth celebration was deliberately set at the time of pagan feasts. A marginal note on a manuscript of the writings of the Syriac biblical commentator Dionysius bar-Salibi states that in ancient times the Christmas holiday was actually shifted from January 6 to December 25 so that it fell on the same date as the pagan Sol Invictus holiday. In the 18th and 19th centuries, Bible scholars spurred on by the new study of comparative religions latched on to this idea. They claimed that because the early Christians didn’t know when Jesus was born, they simply assimilated the pagan solstice festival for their own purposes, claiming it as the time of the Messiah’s birth and celebrating it accordingly.