Assuming that you take it as part of Europe; Greenland has the coldest climate in Europe.
Scandinavia/Northern Europe.
january
Yes
Northern Europe.
Northern Europe has the coldest weather of all of Europe, especially on or near the Arctic coast.
Russia, around Yakutsk and west of the Ural mountains
The capitol of Russia, Moscow, is in Europe and Russia began as a European state. However, more than half of the lands that now constitute Russia are in Asia. So Russia is in both Europe and in Asia.
It borders the Arctic Ocean.
Northeastern Europe is one of the coldest inhabited places on Earth. Southern Europe is the warmest place in all of Europe, so Northeastern Europe is most definitely not warmer than Southern Europe.
I'm quite sure it's Norway, Sweden, Finland and Russia.
Sweden has the lowest temperature ever recorded on the continent at -53˚C (-63.4˚F).