Canada

So the argument is that there's no winning, so no one will play. I can see the appeal in the idea, but doubt its viability. Should the US ever decide to take Canada in whole or in part, it would be through salami tactics (Wikipedia link you want something more serious) rather than a full scale invasion. The Americans could annex Toronto tomorrow and the rest of Canada would be scared and angry for sure, but would we demand that Ottawa launch our nuclear arsenal promising our annihilation? What if the Americans took Ottawa, and Montreal a few weeks later? How 'bout then? Would Alberta even care?

The MAD doctrine was developed as a deterrent to nuclear attacks, not conventional ones. Sure, if the US were to attempt a first strike nuclear volley, having nukes on-hand might deter them from targetting us, but assuming that having nukes would protect us from conventional invasion doesn't make any sense to me.

Consider your reference to Ukraine. If Ukraine had nuclear weapons, what makes you think that Russia wouldn't have annexed Donetsk anyway and claimed "liberation"? They had all manner of cover: local Russian-speaking population, strong separatist factions. They could invade claiming that they're simply "protecting Russian interests/citizens" etc. Would the world expect Ukraine to launch their nukes then? What would be the inevitable outcome of such a choice to both parties? How many Ukranians would be left a few days later?

So now you have a poorly trained local military (all your money has gone to developing and maintaining a nuclear arsenal you don't expect to use after all) and the Russians have taken an entire region and are angling for Kharkiv next. Kiev calls for help from the world community but as their rhetoric is also coloured with threats of nuclear retribution, the world isn't keen on helping either side. Maybe the Russians take Kharkiv because they're feeling audacious and stop there, or maybe they try and Kiev launches a nuke on Moscow and everyone dies. There's no scenario here where nuclear weapons make things better.