This one was set in contemporary (for when the story was written) times. The Soviets and the U.S. have finally had a nuclear war, and both sides have suffered enormously. Part of the sci-fi aspect is found in the nature of the weapons used.
The U.S. had improved upon the so-called "neutron bomb", which was designed to kill people with hard radiation, but leave structures mostly intact. The new bomb design basically caused no conventional damage, but eradicated organic life with terrible efficiency.
The Soviets, in response, developed a bomb that did the opposite. That is, their new nuclear weapon destroyed non-living matter at the subatomic level, but was harmless to human/animal life. The author wrote about the Soviets claiming their weapon was so much more humane than the people-destroying weapons of the West.
The result of the nuclear war, given the weapons, was unique. Every last Soviet had been wiped out, but all of their cities and infrastructure stood as before. No Americans had been killed by the Soviet bombs, but every structure, machine, and so on had been vaporized. Even the clothes they'd been wearing that day. So, America now consisted of 200+ million naked people with no cities, cars, roads, and so on.
The story continues with this implausible premise with most of the rest of the world shunning the U.S. after the war, leaving all the survivors to fend for themselves. The solution to their problems is that, as they need a new home, and there aren't any more people in the USSR, they'll make the long, bitter trek to the Bering Straits and beyond.
As expected, most don't make it. The survivors who do, though, begin to exhibit strange behavior. They increasingly adapt to their new home by adopting the customs of the former occupants. The suggestion is that the U.S. survivors are being "transformed" into Russians by the environs around them. Not sure if that was meant to be a supernatural influence, or just a practical one. The story took a lot of leaps with both science and plausibility.
It came out in the late 70s or very early 80s, IIRC. That would be very much in keeping with the Cold War/nuclear armageddon theme. I am almost certain I read it the old sci-fi magazine Omni.