If you can find the publication "Nuclear War Survival Skills" by Cresson H. Kearny, published by Oak Ridge National Laboratory — it was posted in an HN thread the other day — look to page 23: "Unsurvivable 'nuclear winter' is a discredited theory that, since its conception in 1982, has been used to frighten additional millions..." The document has quite a few "Myth/Facts" items for one's consideration.

Reading Wikipedia regarding the bombings of Hiroshima and Nagasaki should provide some amount of comfort. About a third of their populations died immediately/very soon after the blast. Of those surviving: "the average lifespan of survivors was reduced by only a few months compared to those not exposed to radiation."

So if you live in a big city, the odds are already in your favour. If you live in a smaller city or town, you're probably not going to be nuked anyway.

Radiation falls off exponentially quickly. Hiroshima and Nagasaki were both re-occupied within a year of the bombing.

More than 2000 nuclear bomb tests have taken place. In 1961 alone, 140 tests were conducted. For decades after, forty to sixty nukes a year were detonated. And yet more radiation was sent up into the atmosphere via a few nuclear power plant incidents. And yet we've continued ticking along just fine. The detonation of a few hundred bombs will not have a big global impact. It certainly wouldn't cause anything like a nuclear winter.

Finally, it seems very likely that Russian corruption is so pervasive that it's unlikely that their missiles have been well-maintained. You don't get to be a billionaire oligarch by spending government funding appropriately: you steal it and tell the bosses that, sure, those warheads you never plan to use are in great condition. IMO if the command comes down the line, the missiles will largely fail to launch; and of those that do successfully launch, few will make it to their target, and fewer yet will successfully detonate.