The actual month is not known because birth records were not kept at that time, only death records. The birth wasn't associated with the Pagen holiday that was celebrated on Dec. 25th untill about a century later.
However, it is known that the census and tax collection were at the early part of the year, and that the animals were brought in from the fields in preparation for them to give birth. Therefor Jesus was born in the early spring time.
In Russia and many of the eastern European nations, Christmas is celebrated on January 7th.
The most probable month would be March.