Despite what Hollywood would have you believe, there would be nations that survive a NATO/Russia war. Namely, any nation in the Southern Hemisphere not called Australia or New Zealand. Mother Nature's winds and Father Physic's half lives combine to give unaligned southern hemisphere nations the break of a lifetime. (Or of a species' lifetime I guess?)

All that said, you are absolutely right about "spoils". No one is gonna be thinking about "spoils". Probably top of everyone's list of questions will be, "How many warheads are left? And what remnants of NATO or Russia control them?"

We're talking about two groups who would have conclusively shown they are perfectly willing to use their nuclear arsenals to achieve their goals. That, combined with the fact that their goals would become a whole lot less lofty overnight makes me think the world would become a very precarious place.