It was more like spring time because of the timing & location of shepherds and their flocks in the Biblical stories about his birth. Also the three wise men were following a star in the east that was bright enough to stand out from all the rest, and this usually happens around springtime.
December 25 date was meant to accommodate one or more pagan festivals. That the Christian church picked out to help convert pagans who were accustomed to celebrating Yule or Winter Solstice or, in Roman regions in particular, the Saturnalia or Janus.This date was chosen, and remains, the traditional date for followers of many different Pagan religions to celebrate the rebirth of the sun.
Following the solstice, each succeeding day has slightly more sunlight than the previous day. It was seen as a promise that warmth would return once more to the earth. Numerous pre-Christian Pagan religions honored their gods' birth or rebirth on or about that day. Their deities were typically called: Son of Man, Light of the World, Sun of Righteousness, Bridegroom, and Savior. (Do your Research)
We celebrate on Dec. 25th because earlier Christians reverse engineered a pagan holiday and some of its traditions and mixed it with Christian traditions and called it Jesus's birthday. Note the Bible does not say December 25 is Jesus' birth date nor to celebrate it. By examining the scriptures carefully you can get an idea of what time of year he may have been born and it isn't in December.
Well, in short, nobody really knows when Jesus was born, but we know he was. So if you choose to celebrate please do not be deceived and don’t look down of those who don’t celebrate or acknowledge this day.