Oymyakon/Ojmjakon/Oimyakon, in Siberia, is the coldest permanently inhabited place on earth. The lowest recorded temperature here is -71.2 degrees Celsius. According to Wikipedia this is the lowest officially recorded temperature in the northern hemisphere.
The village has a population of around 800 and is located 690 meters above sea level and lies in a valley between two mountain ranges (the reason for the low temperatures). The name Oymyakon means "non-freezing water" because of the natural hot spring close to the village.

What is there to eat so far north?
All people eat is reindeer and horsemeat. Medics say the reason they don't suffer from malnutrition is that there must be lots of micronutrients in their animals' milk.
There is a short summer season during which people can grow things. But for the most part people don't eat fruit or vegetables.

How do people keep warm?
Fur. Fur is considered a luxury in the West but it is the only thing that keeps you warm.