The "snow country" refers to the northwestern region of Japan, which is famous for hot-spring resorts that are popular for both locals and tourists. This area is near the Japanese Alps, a mountain range that covers extensive areas of Honshu—the main island of Japan. However, the term "snow country" has a poetic denotation in the Japanese language.
In Japanese literature and art, the snow country is often depicted as a place of ghosts, of snow demons, and a place that resembles the Judeo-Christian concept of purgatory or the afterlife. The demons and ghosts in Japanese mythology associated with the snow country are personifications or representations of memory. The nature of memory or one's past haunting them is a recurring theme in Japanese mythology and literature.
Likewise, the winter season symbolizes death, as vegetation in the region are not in bloom during this time of the year. The snow, like sand dunes, can easily cover one's footprints and other signs of life, which represents the erasure of where one has come from and makes ambiguous where one is going. In the novel, Komako's terminally-ill fiance goes to the snow country to die. Likewise, Shimamura goes there to have an affair, as if the snow country is a realm where his second life can exist. Tokyo represents reality for Shimamura—his marriage, his career, etc.—and he goes to the snow country to be with his lover, Komako.
When Komako and Shimamura's affair nears its final days—due to Komako's jealousy and heavy drinking—it is no coincidence that this happens during the transition to autumn, marking the end of the "snow country," or the fantasy land that they had been living in.