The coldest city in the world is Yakutsk in Siberia, Russia. It is the capital of the Sakha region and is less than 300 miles away from the Arctic Circle. While summers can be warm - the average July temperature is about 20C -, a typical level for January is about -40C, and -60 is quite common. It's not actually the coldest place on earth to live - the coldest is another Russian town called Norilsk - but it is the coldest city.
Yakutsk is built on permafrost, so it's a bit like living on top of snow all the time. Most houses are built up on piles to keep well above the cold ground.
In the winter this city is so cold that even wearing glasses out of doors is dangerous, as the metal can freeze and stick to your face. People can get their hands stuck to car doors if they touch them without gloves.

However, the local people are used to the cold and well adapted to it, and the countryside around the city is beautiful.