Though advertisers and merchants would have us believe that the Christmas season begins at Thanksgiving (or possibly Halloween), liturgically it begins on Christmas Eve and extends until Twelfth Night, the eve of the Epiphany. The Twelve Days of Christmas are Christmas through January 5th.
No one knows when Jesus was actually born and the few sources are conflicted. The best guess is it was in the spring (northern hemisphere) sometime between 6 and 4 BCE.
As the Christian faith evolved over several centuries different events were observed — the nativity, the baptism, the epiphany (i.e., the arrival of the Magi). Ultimately January 6th emerged as an important feast, the baptism or revelation of Christ (to the Gentiles) being more significant than his birth. The Roman church came to recognize December 25th for the nativity, possibly to offset the pagan Roman solstice celebration Natalis Solis Invicti.