Responding with nuclear power would be political suicide if it was done today, more so than if Russia invaded northern Norway. Look at Ukraine as one example. Hell, even Drumpf and Rocket man haven't put nuclear bombs to use yet. Hiroshima and Nagasaki will hopefully be the last ones used in war (note I can have missed other nuclear bombs used in war before, point being I hope we don't have to see another).
The backing from the US back then means feck all for if the British soldiers untrained with the climate here would stand a chance against the Russians who had a short way to deliver troops and resources while being used to the same climate.
It's unlikely that Norway and Russia will be in war against each other, my ultimate point is that Russias power was more than enough to take over Norway back then but chose to liberate and help rebuild our region instead. The alliances had more than enough to focus on in Belgium and that region, and wouldn't be able to put significant forces into protecting Norway from the russians, reclaiming is absolutely possible, but protecting is a no-go, at the very least down to the south of Norway, which is a very small part of the country despite being the most populated area.
You've still proved feck all when it comes to it being improbable for the Russians to be able to take over Norway back then through taking over Finnmark and getting foot-in here. Norway was in complete disarray during the nazi-occupation. No proper resistance would fall on the Russians until half the country would have been taken over, regardless of allied forced being able to spare soldiers or not.
