You're forgetting that the US have explicitly stated that in a nuclear war they won't target civilian infrastructure, only military targets. Russia will have had time to prepare and evacuate it's civilians and prep it's landmass to persevere.
Russia existed long before America, it'll still be there long after America is nothing but a bad memory.
Humanity will survive nuclear war no matter how bad it gets, we've survived similar events during the ice age will nothing but wolf pelts and spears. We'll survive nuclear winter - and the great powers of the NWO will fade away in the snow.