It is not unusual for Christianity to absorb some of the previous religious traditions of the newly converted. This happened when Europeans converted to Christianity. Some have suggested that the practice of celebrating Christ's birth on December 25 is a legacy of European paganism.
Its very easy to figure out when Christ was born. According to Luke, John the Baptist was conceived just after the "course of Abia", which was mid-June. He would have been born in March the following year. Christ was 6 mos. younger than John, which would put His birth sometime in late September. I celebrate Christmas as the time of His conception, since that would have occured in late December.