The setting of “Death in the Woods” is a small rural town in the late nineteenth century, “likely based on Anderson’s childhood home of Clyde, Ohio” (enotes historical context). The setting influences the plot because it is a story of a family’s rural life. The old woman lives “on a farm near the town” and comes to town once in a while with an old tired horse. This is a distinct 19th century event. These days the woman would walk or take a bus, because she is likely poor.
The fact that it is a small town also influences the plot, because the woman would not likely be otherwise noticed.
All country and small-town people have seen such old women, but no one knows much about them.
To a certain extent, the story of the woman’s body being found could happen today. It is the rest of her life that is more dependent on the setting.