This is from a Christian website:
http://www.allaboutjesuschrist.org/was-jesus-born-on-december-25-faq.htm
The Bible itself tells us that December 25 is an unlikely date for
His birth. Palestine is very cold in December. It was much too cold
to ask everyone to travel to the city of their fathers to register
for taxes. Also the shepherds were in the fields (Luke 2:8-12).
Shepherds were not in the fields in the winter time. They are in
the fields early in March until early October. This would place
Jesus' birth in the spring or early fall. It is also known that
Jesus lived for 33.5 years and died at the feast of the Passover,
which is at Easter time. He must therefore have been born six
months the other side of Easter - making the date around the
September/October time frames.
Other evidence that December 25 is the wrong date for the birth of
Jesus comes from early writings. Iraneus, born about a century
after Jesus, notes that Jesus was born in the 41st year of the
reign of Augustus. Since Augustus began his reign in the autumn of
43 B.C., this appears to substantiate the birth of Jesus as the
autumn of 2 B.C. Eusebius (A.D. 264-340), the "Father of Church
History," ascribes it to the 42nd year of the reign of Augustus and
the 28th from the subjection of Egypt on the death of Anthony and
Cleopatra. The 42nd year of Augustus ran from the autumn of 2 B.C.
to the autumn of 1 B.C. The subjugation of Egypt into the Roman
Empire occurred in the autumn of 30 B.C. The 28th year extended
from the autumn of 3 B.C. to the autumn of 2 B.C. The only date
that would meet both of these constraints would be the autumn of 2
B.C.
John the Baptist also helps us determine that December 25 is not
the birth of Jesus. Elizabeth, John's mother, was a cousin of Mary.
John began his ministry in the 15th year of Tiberius Caesar. The
minimum age for the ministry was 30. As Augustus died on August 19,
A.D. 14, that was the accession year for Tiberius. If John was born
on April 19-20, 2 B.C., his 30th birthday would have been April
19-20, A.D. 29, or the 15th year of Tiberius. This seems to confirm
the 2 B.C. date, and, since John was 5 months older, this also
confirms an autumn birth date for Jesus.
Another interesting fact comes from Elizabeth herself. She hid
herself for 5 months and then the Angel Gabriel announced to Mary
both Elizabeth's condition and that Mary would also bear a son who
would be called Jesus. Mary went "with haste" to visit Elizabeth,
who was then in the first week of her 6th month, or the 4th week of
Dec., 3 B.C. If Jesus was born 280 days later it would place his
birth on Sept. 29, 2 B.C. Some scholars interpret the 6 months to
be in line with the Hebrew calendar or the August-September time
frame. Since Mary's pregnancy commenced a little before the sixth
month around July, Jesus would be born somewhere around
March-June.
