The Soviets had 36,000 DELIVERABLE nuclear weapons, the U.S. had 23,500. Both sides have jacketed weapons available (actually all that is necessary is to install/attack a pre-made jacket to a regular weapon). The Soviets had deliverable stockpiles of several biological agents, including engineered smallpox and anthrax, various toxins and plant blights. It is entirely possible that every city, on Earth, with a population over 100k is hit by one side or the other (in some cases by BOTH sides). The various oil fields around the world would destroyed, any port that could provide support, even at gunpoint, to either sides naval forces is gone.
500 years or so is if the Soviets and Americans (along with the rest of the nuclear powers) are slightly sane in their targeting and if the Soviets keep Pandora's Box closed.
Both sides go all in and the human race is back to hunter-gathers (in fact it is likely that those groups that remain are the primary source of survivors thanks to lack of contact with the outside world). If the engineered bio-weapons are put in play, with the reality that NO ONE will have any immunity, outside of a few Soviet leaders, a 95%+ die off is entirely possible. Game over.