"The exact date of Jesus' birth is a mystery. About the best we can do is to narrow it down to seasons. The Bible does give us one clue. The shepherds were in the fields with their flocks at night when Jesus was born. This clearly indicates that Jesus was born during the warmer seasons. During the coldest months like December or January, the shepherds didn't sleep in the fields but would bring their flocks into corals. There is virtual agreement among scholars that December 25 is not the birth date, not even the month that Jesus was born.
However some suggest that the whole idea that the flocks where brought into corals during the coldest months, implying the shepherds were not out in the fields, is rejected by some who say the flocks stayed in the fields year round.
"And yet Jewish tradition may here prove both illustrative and helpful. That the Messiah was to be born in Bethlehem, was a settled conviction. Equally so, was the belief , that He was to be revealed from Migdal Eder, 'the tower of the flock.' This Migdal Eder was not the watchtower for the ordinary flocks which pastured on the barren sheepground beyond Bethlehem, but lay close to the town, on the road to Jerusalem. A passage in the Mishnah leads to the conclusion, that the flocks, which pastured there, were destined for Temple-sacrifices, and, accordingly, that the shepherds, who watched over them, were not ordinary shepherds. The latter were under the ban of Rabbinism, on account of their necessary isolation from religious ordinances, and their manner of life, which rendered strict legal observance unlikely, if not absolutely impossible. The same Mishnaic passage also leads us to infer, that these flocks lay out all the year round, since they are spoken of as in the fields thirty days before the Passover -- that is, in the month of February, when in Palestine the average rainfall is nearly greatest. Thus, Jewish tradition in some dim manner apprehended the first revelation of the Messiah from that Migdal Eder, where shepherds watched the Temple-flocks all the year round. Of the deep symbolic significance of such a coincidence, it is needless to speak". (Afred Edersheim in The Life and Times of Jesus The Messiah, p186-187)
The "lambing season" for sheep is in February in Palestine. Could it be an interesting suggestion that Jesus, being the "lamb of the world" was born at exactly the same time the literal lambs were born. If so then Jesus was born when the lambs were born and he died when the Passover lamb was slaughtered on Nissan 14. Of course this is purely speculative.
Another speculative argument is that the census that Caesar Augustus took in Luke 2:1, would not have been done during the coldest harshest season. Such a census would require mass migration of large numbers of the population. Unless Augustus deliberately wanted to make life difficult, he would take such a census during the warmer months and certainly not in December.