In a setting where an empire establishes an island colony far to the north, what is the coldest climate such a colony could sustainably survive were that empire to collapse and stop sending supply ships? This would be without the resources for a nation's worth of powered greenhouses or similar construction projects, and with technology befitting the cold-war era.
Additionally, how large a population could the (ex-)colony continue to hold, if for example it were roughly the size of the British Isles, while still able to sustain things like a military?
My current best guess for how food would be handled is a population dependent on a mix of any fish and birds that can be hunted, additional to farms using great rows of low-lying cold-frame greenhouses. Perhaps they could also farm sheep or other grazing livestock to get what little they can from the grass as well. Could there also be more material-efficient ways of doing agriculture in the coldest possible climate?
Finally, I've assumed that food will always be the limiting factor for the coldest sustainable climate. Could there be a different limiting factor that I'm not aware of?