The Inuit, at least those who survive without constant imports, are more or less entirely carnivorous hunters - which is a lifestyle that can't support terribly large town & city populations. Fish are also very important - inland communities at those latitudes would I think struggle significantly more. Also, seasonal migrations are worth taking into account.
It sounds in your initial description like the fire is something that gets activated rather than being in constant use, which is interesting.
My thought would be, in terms of climate, to make it a bit more just "bloody cold", but introducing some seasonal variation which could make the whole thing make a bit more sense. So in summer things green up a little, there are a few plants growing in the valleys though not a complete thaw in the hills and still with regular snowfall. This is a time when the fire isn't necessary for survival, and indeed poorer communities probably don't use it; in larger settlements it could be an act of euergetism to provide "superfluous" but pleasant fire-domes to the grateful poor. This also solves your food problem if migratory animals are available to stock food up for part but not all of the year, and also this will be when trade routes are open by which the larger settlements send huge quantities of furs and leather south in order to import grain and other agricultural produce (this is basically how the colonies of French Canada worked). Trade is definitely a necessity if you want settlements of any size to make sense here; possibly mining as well as skin trading could explain how the trade balance is sufficient for city-size places to exist? Basing it on imports isn't necessarily impractical, as long as you can explain the trade routes and why it's worth people carting that much food that far north.
In the winter, on the other hand, the weather could get an awful lot more extreme. The fire becomes then a necessary protection for any sizeable settlement to stop raging blizzards; smaller settlements without the fire retreat into igloo-like burrows or caves with heaps of supplies for the worst 2-3 months, existing only extremely precariously, whereas larger settlements with the fire are able to carry on functioning as normal. This is crucial for their more developed economies, especially in tanning and metalwork, which can then carry on rather than halting entirely in the winter months.
Those were my thoughts anyway, hope they make some minimal amount of sense/are helpful as vague suggestions