The Saturnalia may not have had any meaningful link with Christmas, but there was a pagan festival for the solstice which did celebrate the coming of the light and victory over darkness, and it was celebrated on December 25. Instead of a link between Christmas and the Saturnalia scholars suggest that the date of Christmas was a Christian takeover of the feast of Dies Natalis Sol Invictus–the birthday of the Roman sun god Sol.
The problem is– this Roman feast is a late innovation. In the year 278AD (well after Christianity began to burgeon across the empire) the Emporer Aurelian began to promote the cult of Sol Invictus. There is no evidence that the birth of Sol Invictus was celebrated on December 25 until around 360 AD. This is well after the date of Emperor Constantine’s conversion in 315, and during the influence of Julian the Apostate–who attempted to turn back the tide of Christianity and return Rome to its pagan origins. Therefore instead of Christians adopting a pagan holiday and making it their own it’s probably exactly the reverse: the pagans–being threatened by Christianity–copied the Christian celebration. The celebration of the Nativity of Sol Invictus was a late pagan attempt to compete with the celebration of the Nativity of Christ the Lord–the Dayspring from on High and the Sun of Righteousness– on December 25.
So where did the date of Christmas originate? In 386 St John Chrysostom preached a sermon linking the date for Christmas to the date of the Annunciation. He does so in a way that suggests that this was already an established belief. The date of the Annunciation was based on a Jewish tradition that the world was created on March 25. The Jews also believed that a great man would die on the same day as his conception. The date for Jesus Christ’s death was Nisan 15 according to the Jewish calendar, or March 25 according to the Roman calendar. The early Christians (who were of course Jews) concluded that Jesus was therefore conceived on March 25. Thus the day of the world’s creation, and the day of the world’s redemption (and therefore the beginning of the new creation) was March 25.
So Christmas Day cannot be separated from Ladyday–the medieval term for the Feast of the Annunciation. Furthermore, as we now celebrate New Years’ Day just one week from Christmas, (and so celebrate in the Christ child’s birth a new beginning) in the Middle Ages it was not so. From the apostolic age through the Middle Ages, the church continued to battle with the vestiges of paganism (rather than adopting pagan customs) The celebration of the New Year on the first of January was considered a pagan festival, so until 1752 the new year was celebrated in Europe not at the beginning of January but on the Christian date of March 25.
This fact alone gives the lie to the idea that early Christians adopted pagan festivals for their own. Until the eighteenth century they deliberately avoided the pagan new year and celebrated on March 25 instead. So if any mid winter festival is pagan it’s New Year’s Eve –which isn’t on the Christian calendar at all.
What about Frodo Baggins? Tolkien fans the world over celebrate March 25 as a day of celebration by the reading of Tolkien’s work. Why is that? Because the day Frodo Baggins saves the world by delivering the ring into the fires of Mount Doom was (you guessed it) March 25. Ladyday–the feast of the Annunciation and the traditional date for the beginning of the world’s redemption.