The Bible doesn't mention when exactly Jesus was born. 

This means that the exact date of His birth is unknown. On the other hand God's word describes two events surrounding Christ's birth, that lead to the conclusion that it's impossible (or at least very unlikely) for Him to have been born on December 25th.

 

1. It's very unlikely that Caesar Augustus ordered ''all inhabitants of the earth'' to register themselves during winter, for many people would have had to travel long distances during cold and stormy weather (in some areas). - [Luke 2:1-3]

 

2. The shepherds were “living out of doors and keeping watches in the night over their flocks.” Back then, flocks lived in the open air from the week before the Passover (late March) through mid-November. They passed the winter under cover, and from this alone it may be seen that the traditional date for Christmas (December 25th) is unlikely to be right, since the Gospel says that the shepherds were in the fields. - [Luke 2:8]

 

Some christians try to estimate when Jesus was approximately born by counting backwards from his death on Passover, in the spring of the year 33 AD (John 19:14-16). Jesus was about 30 years old when he began his three-and-a-half-year ministry, so he was probably born in the late summer/early fall of 2 BC (Luke 3:23). Although it's still possible that He was born in spring or even in winter (very unlikely - read above).

The bible doesn't clearly tell us a date of birth, so we shouldn't try to find out the exact date by estimates.

Some theologians even think that Jesus might have been born in 7 BC.