There is no chance for survival.
Read Fate of the Earth by Jonathan Schell.
A very limited nuclear exchange of as few as 10 or so ICBMs would result in a nuclear winter of at least three years.
This would destroy agriculture, because there would be no sunlight for that three year period. The planet would be covered with hazy, toxic clouds.
Being isolated in Montana isn't going to save you. It will just mean you'll be even colder than you would have been, so that instead of dealing with 50 below temps, you may be dealing with 100 below.
With wildlife rotting in the fields, pastures, and mountains, you'd be faced with disease at every turn, even without the threat of radioactivity.
A massive exchange of ICBMs would be even worse, and shut down the planet for several hundred years.
There would be no need for a U.S. response. If Russia strikes the U.S with ICBMs, they are striking themselves, too.
Putin has access to the same science as little old me. He has kids, as Sting might say.
That doesn't mean he's not crazy enough to do it, but if he does, it's over for everyone, including him.
Mother earth would recover, and secretly breathe a sigh of relief that we are gone.