If a nuclear exchange breaks out, most of the survivalist skills and equipment may be in vain, in my humble opinion, unless you are willing to live underground for a year or more. How you will survive with the onset of nuclear winter effectively stopping all agriculture and the fact rainfall and snowfall will contain dangerous amounts of radioactive material for at least five to seven years?
Nuclear war is near the bottom of my list of things to worry about. Nuclear war is only possible when one side wants to utterly destroy the other side. However there is no political need for such an action. There was no such need in 20th century, and there is even less now. Any country that wishes for destruction of the USA only needs to buy a calendar.
The only possible threat of nuclear attack comes when the government, in its last and futile attempt to stay in power, uses nuclear weapons against its own country. It's possible - Assad is doing about that right now. He has no nukes, but he has artillery - and the only difference is in time that it takes to level a city. The end result is the same. This is possible because at least one side in that conflict has a strong desire to destroy the other side.
Aside from that, the next likely scenario that the USA may encounter is the economic collapse. As soon as the US dollar is no longer a desirable currency we cannot use it to buy oil. Without oil production and transportation of food will be curtailed (corn will rot in the fields.) Without food there will be riots. Once the riots start there will be National Guard in the streets. Not that it would help any - there isn't enough soldiers in the USA to patrol every street of every town. Perhaps there will be one soldier per town - or one small group of soldiers per hundred towns.
Regardless, once the soldiers are in the streets there will be shootings and there will be even larger riots. In the end soldiers will not be able to hold the ground, and they will retreat because doing anything else would require taking the route of Assad. Nothing less will be effective (see the success in Afghanistan.) If the army is not willing to kill citizens by hundreds of thousands then it might just as well not get involved to begin with. Generals know that. They also know that it's pretty hard for a US soldier to desert in Iraq; but it's trivial here and the soldiers will have plenty of motivation to do so.
IMO, the “Nuclear Winter” theory and even how much radiation for how long rest on a lot of blanket assumptions. The most dangerous period, in terms of radioactivity, would be the first few weeks after, depending on half-lives of radioactive elements and wind patterns.
Vladmir Alexandrov successfully debunked “nuclear winter” just before his disappearance. He analyzed the huge Siberian forest fire and found no global impact. The burning of the wells in Kuwait was likewise examined and found to contribute little to the global environment. Both events put gigatons of stuff into the atmosphere, like a big nuclear war would.
But as an antinuke platform for Sagan et al it just could not be beat.
Fallout is a problem if there are lots of ground bursts, and yes, you’d be under shelter for months if you are downwind of a plume. Got rad detection gear? I suggest an old CD ion chamber for high levels and a classic Geiger-Mueller rig for low level stuff.
Back then there were literally tens of thousands of warheads waiting to go. There are far fewer now, though the number is not insignificant.