The first point to note comes from I Chronicles 24:7-18. The priests were partitioned into 24 divisions each, we assumed (which is confirmed by the Talmud), serving half of a month in the temple, starting with the rust of the year. Zacharias, father of John the Baptist, was of the eighth course, that of Abijah (Lk. 1:5) and would therefore be on duty the last half of the fourth month.
“And it came to pass, that while he executed the priest’s office before God in the course of his order” an angel appeared announcing that Elizabeth, his wife, would conceive a child -John the Baptist (Lk. 1:8-17). Now we assume that the conception occurred upon Zacharias’ returning home at the beginning of the fifth month.
“And in the sixth month (of Elizabeth’s pregnancy which would be the tenth month of the year) the angel Gabriel was sent from God unto a city of Galilee…to a virgin” with the announcement regarding the Christ. Thus in the tenth month of the year, Mary became pregnant by the Holy Spirit and would therefore bring forth Jesus in the seventh month of the following year.
The Jewish year begins in our March or April, depending on the moon. The seventh month can thus be as early as October or as late as November. The weather this time of year is more pleasant for traveling than the heat of summer or cold of winter. Thus the birth of Christ must have been sometime in the fall of the year, rather than the beginning of winter which would be the case if he were born December 25.