Only a few flights actually fly over the north pole, but a lot fly close to it. The world is a sphere and it is the shortest way to get between two points.
I don't know what 'cold air pressure' is. Those planes are flying between 30,000 and 40,000 feet. The air at that altitude is cold and thin whether you are flying over the north pole or the equator, which is why planes are pressurized and heated.
As for landing, every plane is certified to be able to fly a certain time away from a runway (for twin engine planes, it's called ETOPS--you can look it up). It doesn't matte whether it is the Pacific Ocean or the Arctic Ocean, or even remote stretches of land without airfields or with airfields that are closed.