Does it not make perfect sense that God coming to Earth in the flesh would be at the time of “God being with us”? That is the Feast of Tabernacles. It is also known as “the Season of our Joy;” so it makes sense for the angel to tell the shepherds he brings “good tidings of great joy” concerning Jesus’ birth during the joyful season of the Feast of Tabernacles:

The angel said: “Behold, I give to you good tidings of great joy, which shall be to all people. For to you is born today, in the city of David, a Savior, who is Christ the Lord.” (Luke 2:10-11).

Shepherds do not spend the night in the pasture with their sheep after mid-October.