I see the post-nuclear environment in a post-1966 as a curved sliding scale of possibilities. Call it the "nuclear horseshoe" if you will, at least as far as probability goes. On the far end of the scale, you have "total human extinction" from all the second-order effects: nuclear winter, disease outbreaks, famines, civil breakdown, etc. On the near end, you have a "brokenback war" scenario, where due to a variety of factors, the nukes maul the countries involved but don't actually collapse them (at least... not immediately), leaving them with just enough to sort out the remains and keep fighting. Both of these are possible - in so far as we can tell - but seem unlikely. There is, of course, not much point to discussing the "total human extinction" scenario, but the "brokenback war" scenario is extremely underexplored in my experience.
Between these two improbables we have varying levels of national/societal collapse, with all the attendant human dieback that entails. This could range from only the directly engaged countries collapsing, to second-order effects collapsing every nation outside regardless of proximity to the war. Most likely, what we'd see is something of a mix, with all the directly involved countries collapsing, second-order effects collapsing a number of the not-directly-involved, and the rest experiencing some period of instability, hardship, and probable reduction of living standards before managing to orient themselves. Naturally, the largest and most powerful of the survivor states in that last scenario would be the best positioned to dominate the post-nuclear world. Who they actually would be is a matter of speculation.