Technically, Christmas was a tradition only after Jesus, hence the Christ's mass bit there. What was celebrated in Rome was dies natalis Invicti the rebirth/reintroduction of Sol Invictus, their Sun god. When Constantine opted to make Christianity the official religion of the empire, some concessions had to be made. One of which was not messing with the party structure, by party, I mean party :) The early Church moved the presumed birthdate to the 25th (in liturgical practice, not theological debate) to unify the two holy days and ease the transition.