What might a major city in the arctic look like?

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Silicon Valley
I should probably explain why this exists first. This is a fantasy world, not Earth, but it's got about the size, shape, and climate range of Earth. However, the gods (now departed from the world) have messed with terrain features quite a bit. Thanks to divine shenanigans nobody really understands (I go by the Greek system of the gods being able to be spectacularly immature at times), there is a three mile column of zero gravity around the North and South poles, surrounded by a weird bubble that prevents the atmosphere from entering the vacuum but does not bar the movement of people and vehicles. This world has a late 1940s level of vehicular and architectural technology (though they haven't invented jet engines) and a modern level of communications technology, and integrates low level Eberronish magic into technology. These zero gravity wells at the poles are what allows space travel, given the lack of rocket engines powerful enough to exit the atmosphere with any significant payload. This is important, because the only way to get really useful stuff like adamantine, mithril, and some useful magical phlebotinums is to mine it from space. So, despite the pre-Apollo mission tech level, there is enough space traffic to make NASA go berserk with envy. Of course, one can only go into space via the North or South pole.

This gets into why I purport the existence of major cities within the arctic circle. To speak in terms of relative Earth geography for a moment, places like Barrow, Alaska. The ocean is not quite ice free, but it is much better than the surroundings, and an icebreaker will handle it with ease. The snow isn't as bad as more heavily inhabited cities that exist, and one could link the town via heavy railroad traffic, given the massive economic importance of a city that can handle a superpower's access to space. Given that this is the stellar equivalent of New York, Los Angeles, New Orleans, DC, and Houston combined, this is a prime location for a big city.

This is where the question comes in. If we're building a big city, like, at least a million or two people, in a place like Barrow, what might it look like? Aside from months of summer day and winter night, what does the local climate hold in store that civil engineers have to work around? What about railroad and aviation engineers? What challenges does the average civilian face in day to day life from the climate? What stresses does the constant cold put on infrastructure? If I want a subway, an overhead rail system, or a streetcar network, what kind of engineering problems are there from the climate? Can I run a reliable major international airport in this climate? What about military bases, since it is vital to control this city and my approaches to the North Pole? How bad are the psychological effects of two month nights and over half the days being overcast? Are there any challenges or observations I'm not even thinking about?

As a related question, can one build, using late 1940s technology, a passenger and freight railroad system through Antarctica, or is the continent too unstable?
 
On the inside it would look industrial shipwrights and merchants would be popular* the city would be built to be as defendable as possible it would also be built to be as insulated and energy efficient as possible because all the fortifications in the world are useless if the occupants freeze to death. The biggest engineering problem you'll face is permafrost increasing the difficulty for building underground, there's going to be two 'seasons' winter and construction. For a subway you're going to have to deal with removing permafrost however the subway would be more secure and protected if military conflict is common, plus they can serve as bunkers if a conflict turns into the London blitz; for the streetcar you'll need to deal with snowfall and ice plus the risk of damage from a military conflict; for the overhead rail system you need to deal with supporting the rail with permafrost and again the potential threat of destruction if military conflict is common**. I believe international airports can be operated in the climate you're , Fairbanks international is in the middle of Alaska. As for military bases look to Canada, Russia, Denmark or Norway.
*during a gold rush you don't search for gold, you sell shovels
**if military conflict is common, make subways and make them deep
 
What challenges does the average civilian face in day to day life from the climate? What stresses does the constant cold put on infrastructure? Can I run a reliable major international airport in this climate? How bad are the psychological effects of two month nights and over half the days being overcast? Are there any challenges or observations I'm not even thinking about?
-challenges: hypothermia, frostbite, common cold, etc.
-stresses: cold, wind, snow build up, etc.
-you can run a major international airport, it won't be reliable
-psychological effects: being miserable all the time
 
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The Alaskan Railroad proves one can build a heavy railroad in extreme northern conditions. The northern Eielson Air Force base proves you can run an international airport. As long as you have access to coal, you can live this far north. The largest concern is hypothermia for new people to the far north, and depression is common this far north.
 
As a related question, can one build, using late 1940s technology, a passenger and freight railroad system through Antarctica, or is the continent too unstable?

No, glaciers can move at ten miles or more per year, breaking up any road or railway in short order.

You could have multi-vehicle tracked snow trains, like this but more steam-punky:




 
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