Most serious Bible students realize that Jesus was not born on December 25th. The shepherds had their flocks in open field  which implies a date prior to October. Furthermore, no competent Roman administrator would require registration involving travel during the season when Judea was impassable.
Why December 25th?
The early Christian church did not celebrate Jesus' birth, and therefore the exact date has not been preserved in festivals. The first recorded mention of December 25 is in the Calendar of Philocalus (354 A.D.) which assumed Jesus' birth to be Friday, December 25, 1 A.D.
December 25th was officially proclaimed by the church fathers in 440 A.D. as a vestige of the Roman holiday of Saturnalia, observed near the winter solstice, which was among the many pagan traditions inherited from the earlier Babylonian priesthood.
But just when was Jesus born. Although the Bible doesn't explicitly identify the birthday of our Lord, many scholars have developed diverse opinions as to the likely birthday of Jesus. (It reminds one of the rabbinical observation: with two Jews, you have three opinions!)
The Year of Jesus' Birth
The year of Jesus' birth is broadly accepted as 4 B.C., primarily from erroneous conclusions derived from Josephus' recording of an eclipse, assumed to be on March 13, 4 B.C., "shortly before Herod died." There are a number of problems with this in addition, to the fact that it was more likely the eclipse was on December 29, 1 .B.C. Considerable time elapsed between Jesus' birth and Herod's death since the family fled to Egypt to escape Herod' edict and they didn't return until after Herod's death. Furthermore, Herod died on January 14, 1 B.C.
Tertullian, (born about 160 A.D.) stated that Augustus began to rule 41 years before the birth of Jesus and died 15 years after that event.
Augustus' died on August 19, 14 A.D., placing Jesus' birth at 2. B.C.
 Tertullian also notes that Jesus was born 28 years after the death of Cleopatra in 30 B.C., which is consistent with a date of 2 B.C.
Iraneus, born about a century after Jesus, also notes that the Lord was born in the 41st year of the reign of Augustus. Since Augustus began his reign in the autumn of 43 B.C., this also appears to substantiate the birth in 2 B.C.
Eusebius (264-340 A.D.), 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
One approach to determining the date of Jesus' birth is from information about John the Baptist. Elizabeth, John's mother, was a cousin of Mary and the wife of a priest named Zacharias, who was the "course" of Abijah.  (Priests were divided into 24 courses  and each course officiated in the Temple for one week, from Sabbath to Sabbath.)
When the Temple was destroyed by Titus on August 5, 70 A.D., the first course of priests had just taken office.  Since the course of Abijah was the 8th course, we can track backwards and determine that Zacharias ended his duties on July 13, 3 B.C. If the birth of John took place 280 days later, it would have been on April 19-20, 2 B.C., precisely on Passover of that year.
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, 14 A.D., 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, 29 A.D., 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 the autumn birthdate for Jesus.
John's repeated introduction of Jesus as "The Lamb of God"  is interesting if John was indeed born on Passover.
The Date of Jesus' Birth
Elizabeth 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 December, 3 B.C. If Jesus was born 280 days later it would place his birth on September 29, 2 B.C.
If Jesus was born on September 29, 2 B.C., it is interesting to note that in that year this was also the 1st of Tishri, the day of the Feast of Trumpets. 
Notes: (clicking on note number returns to related text)
 Luke 2:8.
 Matthew 24:20.
 Alexander Hislop, The Two Babylons, Loizeaux, Neptune NJ, 1916.
 Matthew 2:15, 19-22.
 Magillath Ta'anith, an ancient Jewish scroll contemporary with Jesus.
 Tert. adv Judaeous, c.8.
 No year 0 between B.C. and A.D.
 Eccle. Hist., i.5. 9.
 Luke 1:5, 8-13, 23-24.
 1 Chronicles 24:7-19.
 Both the Talmud and Josephus confirm this.
 Luke 3:1.
 Numbers 4:3.
 John 1:29, 36.
 Chuck Missler, Personal Update, August/September 1992.