Its Christmas time - The time of the Birth of Jesus or.... not?

I have no doubt about the existence of God our universal creator of life. With Christmas day fast approaching the birth of Jesus will be celebrated by many. However there is some doubt that Jesus was born on the 25th December. There are several references in the Bible that make it unlikely that Jesus was born on this day. One small example of this is that in Luke it is mentioned that the Shepherds were in the fields at the time of his birth. December in Palestine is winter and would have been far too cold. They are in the fields early in March until early October. This would mean that Jesus was most likely born in September in Spring or March in Autumn.. Records state that Jesus died at the age of 33 and a half at the feast of the Passover, which is at Easter time. This would make his birth around September/October time. December 25 was chosen as the day to celebrate Christ's birth around the 4th Century. December 25 was already being celebrated by pagans as the day of the Sun God so this dual celebration was thought to make Christianity more appealing to the pagans. If you look at 25/12 on its own. it is not a significant number but does reduce to the number 1. The number one as we know is leadership, originality, new beginnings which is fitting but not of great significance on its own. There no doubt that the birth of Jesus is of paramount spiritual significance to all Christians but it is unlikely he was actually born on that day.