I remember studying this in history class. I don't think we know for certain, but back in the Roman Empire times they had a holiday around the time of December 25th. It was to celebrate Winter and wanting to have a good Spring harvest. They gave gifts, danced, ate good food and other stuff. This was all way before the time of Jesus.
They used green a lot because it as about wanting lots of things to grow in the Spring. The red part is not that clear. Some say it was also a fertility ritual, and red and green are opposite colors representing men and women. The white color probably represents snow. They put them together as a way of praying for a fertile spring.
Much later, this time of year was connected with a lot more meaning after Jesus came and they kept the same red/green colors.
