In the case of "The Moose and the Sparrow," we get one major clue as to the location of the story's action. The narrator says,
That summer we were cutting big stuff in an almost inaccessible stand of Douglas fir about fifty miles out of Nanaimo.
Nanaimo is a city in British Columbia, Canada, on the coast of Vancouver Island. At one point in the story, Moose asks Cecil what he does on the "mainland," so we can understand that the story takes place in a logging camp on Vancouver Island somewhere.
As far as when the story takes place, we may have to investigate some more clues in terms of the actual history of the area. The narrator mentions that the mail is "flown out every week," so we know that the story must take place at some point in the twentieth century (because of the reference to airplanes). In addition, we learn that Cecil originally began his work as a "whistle punk," someone whose job it was, during the logging industry's heyday, to operate a signal that communicated to other workers that a log was loaded and ready to move. This heyday, in Vancouver, took place in the 1950s, so it is reasonable to assume that the story takes place around the middle of the twentieth century.