Literally the coldest place in Japan would be the summit of Mt.
Fuji, however people don't permanently inhabit this area and it is
a at a very high altitude.
The coldest inhabited low lying area in Japan is found on the
northern island of Hokkaido, a place known as Rikubetsu. Night time
temperatures average lower than -20℃, with temperatures frequently
as low as -30℃.
Most of central Hokkaido averages night-time low temperatures
below -15℃ and usually don't rise above -4℃ in the day. The climate
of this area in Japan falls under the Humid Continental
classification, though bordering very closely with Subarctic.
Some settlements found at higher altitudes on the mainland of
Japan, mainly in and around the Northern Japanese Alps can be
extremely cold. Shokawa, a village located in the outer reaches of
Takayama City averages a night time low temperature of around -13℃
during February, but however due to its location and elevation
experiences much more in the way of heavy snow and strong wind in
comparison to that of Central and Eastern Hokkaido.
These areas of the Northern Alps can indeed feel much colder due
to the significant wind chill and wilder mountain weather.
Similar climate is found in parts of Canada including Quebec and
Ontario.