Was Jesus really born on 25th of December?

Tens of million people around the world today celebrate the death of Jesus christ on the 25th of December each year. But this remarkable date “December 25”, is it truly the day the Jesus was born? Let's take a look at some details.
The foremost thing we know is that the Bible does not state what day or date Jesus was given birth too.
First, to state some few notable quotes;

McClintock and Strong’s Cyclopedia -
The day of Christ’s birth cannot be ascertained from the N[ew] T[estament] or, indeed, from any other source,

The exact date of Christ’s birth is not known.
—Encyclopedia of Early Christianity

The true birth date of Christ is unknown.
—New Catholic Encyclopedia.

Since the Bible doesn't give the answer as to when Jesus was born, it describes some events or activities that happened during the birth of Jesus christ that shows that December 25 isn't the day of birth of Jesus.

• The registration of citizens
  Shortly before Jesus was born, Caesar Augustus issued a decree ordering “all the inhabited earth to be registered.” Everyone had to register in “In his own city,” which might have required a journey of a week or more. (Luke 2:1-3) That order—probably made to support taxation and military conscription—would have been unpopular at any time of year, but it is unlikely that Augustus would have provoked his subjects further by forcing many of them to make long trips during the cold winter.

• The sheep.
  Shepherds were “living out of doors and keeping watches in the night over their flocks.” (Luke 2:8) The book Daily Life in the Time of Jesus notes that flocks lived in the open air from “the week before the Passover [late March]” through mid-November. It then adds: “They passed the winter under cover; and from this alone it may be seen that the traditional date for Christmas, in the winter, is unlikely to be right, since the Gospel says that the shepherds were in the fields."

• Calculations of Jesus age from time of death
  We can estimate when Jesus was born by counting backward from his death on Passover, Nisan 14 in the spring of the year 33 C.E. (John 19:14-16) Jesus was about 30 years old when he began his three-and-a-half-year ministry, so he was born in the early fall of 2 B.C.E.—Luke 3:23

• Let's also take a look at another fascinating fact from Elizabeth. She obnubilated 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 pregnancy commenced a little afore the sixth month around July, Jesus would be born somewhere around March-June.

Conclusion
It would've been too much from Caesar Augustus was to ask everyone to travel to the city of their fathers to register for taxes in the cold. Also the shepherds were in the fields and shepherds were not in the fields in the winter time. They are in the fields early in March until early October. Also too is the from the case study of Elizabeth.

Reference materials
Jw.org
Allaboutjesuschrist.org