The course of Abiah, see First Chronicles Chapter 24. It is all about the time when Moses setup the Priesthood line of Aaron to tend to the burnt offerings at the stone altar which was in the form of a large triangle. Afterwards when Solomon's temple was built to house the Ark of the Covenant, the priests continued their courses alotted and the traditions of the burnt sacrifices and ministered to the people. This continued on to the second temple that Zacharias attended in his time. Remember when they drew lots and the year was then divided into 24 courses? One course is 15 days. Luke 1:5. here we learn that Elizabeth is one of the daughters of Aaron which makes Mary a daughter or descendant of Aaron as well because the mothers of Elizabeth and Mary were sisters. Zacharias during his course of Abiah which was nearly done by our calendar is about June 20th when he left for his home which is away from Jerusalem. We surmise here that it may have taken one to three days to get home as we are not told where at the time Zacharias is living. Nonetheless, verse 24 is another key as we learn that after Zacharias' return, Elizabeth is then with child FIVE MONTHS which would be about November 24. Then we learn that an Angel appears to Mary in Narareth and at that time it is the SIXTH MONTH for Elizabeth which is about December 25th. There is a lot more to this story, but I think you can figure it out from here. I used to give lectures in advanced Biblical studies many years ago in seminaries and Colleges and this was one important subject for every Christian to know. Its great that you figured out that the shepherds did not tend their flocks in the fields in December, the grass is dead and its cold.