And even Hanukkah is a December 25th event as well, at it's roots, anyway...
The festival of lights that Jesus attended in John 10 was, practically all scholars agree, Hanukkah.
It was December 25th, 165 BC when the Macabees cleansed the temple and the jar of oil lasted 8 days.
The pagans and other godless peoples of course understood that there was something unique about the winter solstice... the longest night of the year, the most dark time on the yearly calendar.... so they had their celebrations long about that time. Saturnalia was celebrated from December 17th to the 24th.
But it's interesting that Hanukkah comes in at that same time, a festival of lights is called thereafter... lights during the darkest time of the year.
What better time for the True Light of the World to come to us?
One of the links I provided above points out that it has actually been in recent times that the December 25th date has come into question... that for centuries no one supposed any other date.
The pages are worth at least a look. One of them actually is written by a guy who does not agree with the December 25th date, but he sets forth quite a good bit of evidence to support it anyway.
So whether we believe it was December 25th or some other date, it doesn't matter. The Bible does not mention the date, and we of course should not part company over the matter. Both sides have their points worth considering...