I think you're both underestimating the abilities of the Soviet Air Force, and the number of nukes it takes to devastate a region. The Soviets don't need full nuclear parity, but if they slag primary sites in Western Europe and the east and west coasts of the US then the fallout alone will take care of the rest. At the same time Eastern Europe and the major sites within the USSR are going to get hit. Therefore, the northern hemisphere is fucked. Even in a 'short' nuclear winter the fall damage alone would take decades to fully heal.
Did you get your idea of fallout from the movie "On The Beach," perchance?