Don't forget South America and Africa. Also the idea of a nuclear generated nuclear winter was an idea populated in the 80s by some models that weren't exactly conclusive. Remember that nukes are likely to be exploded over targets rather than in the Earth, and Krakatoa was literally earth being blown up. One caused a slightly cold summer. It had the yield f 13,000 Little Boys or 4 Tsar Bomba, or about 80 tactical nukes. So we are talking similar scale.
Obviously this is comedy, but fun fact for future reference. Nuclear winter is probably not a thing.
The idea of nuclear winter is the distribution of the explosions sending large amounts of dust into the atmosphere to reflect sunlight back out of the atmosphere before reaching earth. A single point explosion, like a large volcanic eruption, wouldn't be as effective even if it is technically a stronger explosion.
That said, I think it would have to be triggered by entire nations stockpiles, namely the US and Russia, triggered by successful dead mans switches. I think there's too many points of failure for all that to be successful.
Oh man, that takes me waaaaay back. Forgot about this video