Do passenger air jets fly over the North Pole often on their way to other side of world (Ex. China) from North America?

Was watching a documentary where someone left Canada on a passenger jet and they showed the flight going over the north pole to China

would it not be kind of dangerous if they had to land and had to get out at the North pole?

Added (1). the cold air pressure is not too much for passengers inside?

Planes fly over the Northern frozen area (near the north pole) all the time. It is no more dangerous than flying across the Pacific Ocean. The percentage of planes which have had emergencies where they had to land immediately, as opposed to diverting to the nearest airstrip, is minuscule at best.

Not quite, but close to it. A MAP makes it seem like the best way to get to somewhere is a straight line, but on a globe, the shortest way to someplace is often an arc.

I used to work on the north slope in Alaska, I used to see planes taking to polar route everyday. Why is flying over the polar ice cap any more dangerous than flying over the open ocean? For a passenger jet the only safe place to land is at an airport with a runway. If you tried to set one down in say a farmers field, odds are it won't end well for the occupants of the plane.

From an air travel perspective you need to think of the earth as a sphere, you take whatever the shortest distance is between two points regardless of what your crossing over (unless it's hostile territory where someone might shoot you down).

Read this

The air temp at 35,000 feet is no colder at the north pole than over the equator. It is not at all dangerous for flying.

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.

Over the POLE? Not very often.

Over the Arctic region? YES everyday.

Would it not be kind of dangerous if they had to land and had to get out at the North pole?

YES as there are no Airports or runways it would be a crash landing.

The cold? The inside of the plane is heated. Of course you already know the normal Air temperature for a flight of thousands of miles is often below zero it is cold up high. The ground temperature is just a concern if you are landing.

You can easily see route approximations on Google map. Use the measure distance feature and just pick two places.

A flight from Seattle to China flies mostly over land. Alaska(Anchorage) then Russia. For political reasons the plane may avoid Russian Airspace and go along the Asian Coast.

A direct flight from Seattle to Moscow would go near the North pole.

The flight path from North America to Asia tend to be South of the pole over Northern Canada and Alaska

Planes have been flying the Polar routes for 60 years.

Airlines are well aware of the available places they can divert to if they must. It does happen and Airports already have arrangements for that rare event.

Between 30,000 and 40,000 feet (9,000 and 12,000 m), the cruising altitude of most jet aircraft, air temperature ranges from -40° F to -70° F (-40° C to -57° C). Modern aircraft have sealed cabins and heaters to protect pilots and passengers from wind blast and cold air.

If you survive the landing on the ocean, the ice flow or some large ice sheet in the Arctic the ground weather might be a concern before rescue comes to you. It does take a few hours for rescue to come from the various places along the routes.

Agreement on Cooperation on Aeronautical and Maritime Search and Rescue in the Arctic is an international treaty concluded among the member states of the Arctic Council - Canada, Denmark, Finland, Iceland, Norway, Russia, Sweden and the United States - on 12 May 2011 in Nuuk, Greenland

For your to China flight most of the way is the responsibility of Canada and USA for rescue.

https://www.myyellowknifenow.com/39134/delta-flight-makes-unplanned-stop-in-yellowknife/

https://www.ktuu.com/content/news/Flight-to-Hong-Kong-diverted-to-Anchorage-468105743.html

Planes routinely fly greater distances over the Atlantic and Pacific without anywhere to land. The arctic circle is relatively unpopulated and it is unlikely that there are any international flights from Baffin Bay to Murmansk across the pole for example.

We actually flew over the north pole flying from Toronto to Beijing. It is faster to go that way. I would say that today's engines are more reliable and even 2 engine aircraft can still fly with 1 engine if something happened to the other one. As for being cold, you don't feel it. Even if you were not flying over the North Pole, when you are flying at 35,000 feet, the air is still super cold.