I think in any of those scenarios, you, us and OUR southern brothers would all become North Americans. And really, even if Russians, and I have to believe only Russians would be capable of attempting this enterprise, what is there to be gained? Are they going to strip our natural resources and somehow take them back to mother? Who’s gonna do that for them? Their army that just fought its way across hell, only now to be expected to not only learn how to mine, defend their new prizes AND figure out how to do it all with half a billion angry North Americans less than a little likely to want to share much less give their sh*t to some asshats? I’m ready, but I still sleep like a baby. ( up twice a night to pee or change my diaper, dreaming about boobs, lol)For us here in Canada, the situation could be much different. If the Ruskies come over the Pole with a land invasion they're gonna have to bolster their advance with strategic nukes. There is no way the US and Canadian forces will allow them to wander all over the nether regions, like in Ukraine. Btw...if they had any idea to do it, they better get at it. Canada is beginning to gear up and if Trudeau gets booted next election and a Conservative government is elected, you can guarantee military spending and recruiting is going to skyrocket up here.
My gut tells me that in such a scenario, Canada will be a very bloody battleground. The US will do everything in it's power to halt a Russian advance at or even well north of the 49th parallel. Anything less would be unacceptable I'm sure. There is also critical infrastructure here, that if captured or destroyed would bring significant hardship to not only Canada but also the US...think natural gas, oil and hydro electricity...lots of it flows south from here.
Also, in order to cross hundreds of miles of tundra and muskeg in northern Canada...the invasion would have to be in winter....BRRRR! That is, if they don't want to be locked into using the Alaska highway and two or three other main roads into the far north. I honestly don't know if it's possible for an invading force to do it...it would be a long and extremely perilous haul for the invaders.
If invaders came from the west or east coasts...again it would depend but fleeing north may be desirable as it is such a vast expanse of territory. But, not entirely hospitable. If coastal invaders wandered north it would be to secure critical infrastructure like water sources for hydro electric and oil and gas. There are no large cities or strongholds to conquer in the Canadian north. There would only be the threat of the US raining down hell from Alaska.
So, fleeing south to the US from here may be the only option. If fleeing was not an option then as others have said...throw a monkey wrench in the works. Create havoc. Hit and run if you can. What else can you do outside of organized resistance or insurgency?