The Bible doesn't mention the birth date of Jesus. It probably wasn't in winter, because shepherds would not be tending their flocks in wintertime.
The simple reason we celebrate it on December 25th is because, in the 4th century, Pope Julius 1, said so. Christianity had become the official religion of Rome, and he declared that the birth of Jesus should be a holiday.
Okay. But why the 25th? Well, Julius was no dummy. There were already festive celebrations during that time all around the world – celebrations of the winter solstice by pagens. In Scandanavian countries, for example, the pagen holiday was known as "Yule" during which a log was burned from the 21st until the new year.
So, Julius basically usurped the already-existing pagen holiday. No other reason. The choice of date certainly had nothing to do with Christ's birth. Instead, it was a calculated attempt to change the nature of already-existing celebrations.
Over the course of several centuries, the choice of date finally paid off, and by the Middle Ages, this time of year was known more for its Christmas celebrations, rather than pagen celebrations.
Christmas trees didn't come onto the scene until the 16th century (a German custom which caught on), and Santa Claus didn't arrive until the late 1700's-early 1800's (originating from the Dutch's Sinter Klaas). Rudoph, of course, was non-existent until 1939.
So remember, Christmas celebration has its roots in pagen festivities having nothing to do with Christ's birth.
Just my little contribution to the War on Christmas.