Was Jesus born on December 25th? No. The Roman Catholic Church adopted this date to take away from the worship of the pagan myth Saturn on this date (among other false gods that were supposedly born or celebrated on this date). It wasn't until A.D. 440 that they officially proclaimed December 25th as the birth date of Christ.
But could Christ have been conceived on that date? Yes. The evidence to His birth date remains with the shepherds, who were keeping watch of their flocks. "And there were in the same country shepherds abiding in the field, keeping watch over their flock by night." (Luke 2:8) Shepherds, watching over their flocks in fields just east of Bethlehem, were the first people told of the birth of Jesus. In December Palestine is very cold. Shepherds were not in the fields during the winter time. They are in the fields early in March until early October. This would place Jesus' birth in the spring or early fall. It is agreed upon by most scholars that Jesus lived for 33.5 years and died at the feast of the Passover, which is at Easter time. He must therefore have been born six months the other side of Easter - making the date around the September/October time frames. 