At the very beginning of the story, we read:
On December third, the wind changed overnight and it was winter. Until then the autumn had been mellow, soft. The earth was rich where the plow had turned it.
This indicates that the season is the cusp between late fall and the start of winter. The calendar has not yet marked the official beginning of winter, but the area is experiencing a sudden cold snap in early December.
On the first night described in the story, Nat Hocken opens a rattling window and is attacked by birds; cries from his children's bedrooms alert him that they are under attack as well. The next morning, Nat looks out on the peninsula where the action of the story takes place:
Nat went to the window and looked out. The sky was hard and leaden, and the brown hills that had gleamed in the sun the day before looked dark and bare. Black winter had descended in a single night.
In this way, we see that the sudden change in the season echoes the sudden strange actions of the birds, and adds a level of foreboding to the atmosphere of the story.