Scientists have discovered an Earth-like planet in another solar system, with the same gravity, atmosphere composition, etc, and they decide to colonize it. There is only one problem, though. It is beyond the Goldilocks zone. Not so far as to make it completely uninhabitable, but enough to freeze the whole surface. There is an underground lake deep under the surface, so water would not be a problem. Would it be possible to sustain towns, and even cities, when the only season is winter? Could it even be remotely plausible?
The same atmospheric composition must mean that there is life already - presumably a Great Oxygenation Event has happened.
Indeed, 'Snowball Earth' is the term given to our planet when it was completely covered in ice, glaciers and snow, for a period spanning over 300 million years. During this period life existed in many niches and in fact thrived, with evidence of microbial life (photosynthesising from within ice), hydrothermal vents, geothermal hotspots and underwater lakes.
In your situation the planet will still have some geothermal energy for which could be used to sustain your community quite adequately. Rarely do you get a planet without some form of molten core or magma - particularly in your case when the planet is similar in composition. This would be a good power source to heat your city and crops, if surface solar panels or wind power is insufficient.
Regardless life would still be able to exist in the niches above too.
So your frozen metropolis is very easy to thrive, in fact if we can journey through the vacuum of space, we can easily exist on frozen worlds.
Not a problem.
You only going to need an energy source. If can be arrays of solar panels, wind turbines, nuclear, or more futuristically, thermonuclear reactors, or anything else. As long as the environment is not particularly hostile (too hot, high radiation, high gravity etc.) and you have access to necessary elements (hydrogen, carbon, nitrogen, oxygen, they even can be imported), your colony is good to go.
Inside a dome (or another type of enclosed habitat) a comfortable temperature can be maintained, and all necessary foods can be grown. The outdoors can be a frozen winterland, but indoors you can house as many people as your energy resources will allow.