Even if they weren't using a 12 month calender, they did use the month of December and they did have the 25th day of that month.
Long ago in Babylon, the celebration for the Son of Isis was celebrated on December 25. This was the origin of the feasting and gift giving.
In Rome, the Winter Solstice was celebrated many years before the supposed birth of Christ. The Romans called their winter holiday Saturnalia, honoring the God of Agriculture where they travelled from house to house to sing . This was the origin of carols.
The pagans of northern Europe celebrated the Yule, symbolic of the Sun God, Mithras. It was customary to light a candle and kiss under the mistletoe. Druids used large evergreen trees as religious symbols.
In the year 350, Pope Julius I announced that Christ’s birth would be celebrated on December 25 because most people at that time were Pagans (atleast in Rome) who celebrated their feasts on that day. By doing this, the conversion into Christianity would be easier.