The earliest historical source that exists which places a pagan holiday on December 25 is the proclamation by Roman Emperor Aurelian of a celebration of Sol Invictus on that day in 274 CE.20 The earliest Christian reference to December 25 as the birth of Christ, however, dates from 202 CE. ...
Given that Aurelian’s religious reforms, like those of Julian the Apostate a century later, seem largely to have been an attempt to undermine Christianity by introducing popular elements of it into paganism, thereby theoretically making paganism more attractive, it seems far more probable that Aurelian’s institution of a celebration of Sol Invictus on December 25 was an attempt to usurp a Christian holiday already established and widely celebrated on that date, rather than the reverse.
A primary concern amongst early Christians was establishing an accurate and uniform date for the celebration of Pascha.22 Various formulas and historical sources were put forward by early Christians in their attempts to achieve this goal. By the third century, two dates had emerged as standard among Christians; in the West 25 March (you may have noted this date in the quote above from St. Hippolytus of Rome) became the standard date for Christ’s death and in the East Christians believed Christ to have died on 6 April.23
Drawing upon an ancient Jewish tradition that holds that a prophet enters life (that is, is conceived) and leaves it (that is, dies) on the same day, Christians concluded that Christ must have also been conceived on 25 March or 6 April (depending upon which date was held to).24 Exactly nine months (the duration of a “perfect” human pregnancy) after 25 March is 25 December; exactly nine months after 6 April is 6 January. As a result, Christians came to commemorate Christ’s birth on these two dates; in the West the former was celebrated and in the East the latter.
TL;DR:To summarize: Even though Western Christians celebrate Christmas on 25 December and most Orthodox Christians celebrate it on 7 January (which is also 25 December) and some Orthodox Christians celebrate it on 25 December, all Christians (except the Armenians!) celebrate Christmas on 25 December. Complicated stuff? Yeah, a little…
1) There's good evidence that the pagan holidays started after Christians began celebrating Christmas on that date.
2) Christmas's date was determined by an old Jewish ritual and the date of the Resurrection.
3) The Old Calendar's December 25 may be the civil calendar's January 7, but we all celebrate Christmas on December 25.