At the time that the angel announced His birth to the shepherds of Bethlehem, they were feeding their flocks by night in the open fields [see Luke 2:8]. It was not the custom for the shepherds of Judea to watch their flocks in the open fields later than about the end of October.
Torah requires its adherents to sacrifice animal every day, morning and twilight.
Now this is what you shall offer on the altar: two one year old lambs each day, continuously. The one lamb you shall offer in the morning and the other lamb you shall offer at twilight; (Exodus 29:38-39)
This verses created a real need of two lambs (young sheep) in Jerusalem every day in any weather, including December weather. However, citizens were prohibited from raising sheep inside Jerusalem.
One may not raise small cattle [i.e., sheep, goats, etc.] in the Land of Israel, but one may do so in Syria or in the uninhabited parts of the Land of Israel (Mishna Baba Kama 7)1
The sheep farming, which are located close to the highway to Jerusalem, on Bethlehem pasture, supplied and met the daily need.
The ritual of animal sacrifice needed sheep every day in any season, weather, temperature, and month; and the sheep farming on Bethlehem pasture was always there to meet the need. Here is a reason for the presence of shepherds and their sheep on Bethlehem fields in December.
The shepherds of Judea watched their flocks in the open fields in any month, including December, to meet the need of daily sacrificial lambs in Jerusalem, near the pasture.
1) http://www.jewishvirtuallibrary.org/jsource/judaica/ejud_0002_0005_0_04581.html. January 9, 2015. 11:49