We also have to overcome the Sino / Soviet Basselope Gap.
That’s some of the conclusions we came to as well. Take a US soldier out of their uniform and put a Canadian in it, and how do you tell the difference? We’d just put on southern accents and pretend we were from Georgia (and remember not to say “eh” all the time).
Would you really want a Canada that’s had its 20 major cities nuked? There wouldn’t be much left here that would be worth having, with everything irradiated. Plus like rogerbox says, there’s all the fallout going straight south - that’s a real bummer, too.
Okay, forget Canada (as we usually do). Back to my other hypothetical, Sweden.
Even if we wanted to invade and conquer Sweden (we don’t! Who WOULD?), we’d need months of prepatration AND a neighboring land who’d let us use them as a launching off point. Who’s going to do that? NOBODY! Which means that, even IF we had an army large enough to subjugate Sweden, we still couldn’t launch an invasion! We wouldn’t have any allies willing to serve as a staging ground.
Finally, I’m reminded of a line in John Wayne’s The Searchers. “This is either a job for a whole company of Rangers or it’s a job for one or two men. As it is, we’re both too many AND not enough.”
Sounds like a pretty fair summary of US military capability. As I said earlier, we can put 100,000 armed men almost anywhere in a hurry… unfortunately, 100,000 men is frequently just enough to get us in trouble but not NEARLY enough to accomplish our goals. Our armed forces are often “too many AND not enough.”
No, we’d just have to invade Norway and move from there.
Actually, such thinking is part of world war strategy. Including, as one component in the original plan, the invasion of Iraq, viewed in the long run vis-a-vis Iran.
But Norway is a NATO member, so if they’re attacked you’d be obligated to defend them. 
I just saw The Mikado last night, and your post reminded me of Ko-Ko’s dilemna.