Any other recommendations in the genre (Cold War-era, post nuclear exchange)?
Most of what I have read is immediately post-exchange....or very longterm, like
Star Man's Son, or
A Canticle for Leibowitz. Of the "medium term" ones I have, you can't beat Zelazny's classic
Damnation Alley (VERY little in common with the film!!!), or the "pre-timeslip" Survivalist books by Jerry Ahern

All excellent romps...but avoid the SECOND half of the Survivalist series like the plague!
My personal faves are the WWIII-type - little gems like Eric Harry's
Arc Light, or any of the Harold Coyle or Larry Bond military fiction. But
Arc Light is the best IMHO.
But there is ONE interesting little number to keep an eye open for - it's called First Angel, and published on the Star label maybe 15 years ago now...by Soldier of Fortune Magazine!
Suprisingly for its origins, it's WELL worth grabbing if you see it. There's also a British-flavoured WWIII novel called Chieftains by one Bob Forrest-Webb on the Futura label, and well over 20 years old now, and only one edition....but if you ever see it, grab it with both hands! And David Graham's "Down To A Sunless Sea" which is great - except for the very last paragraph!
Moving more into the medium to long-term future again....and thus verging on sci-fi...also keep an eye for any of Edgar Pangborn's old "
Davy" series -
Davy,
The Company Of Glory etc. an Eastern Seaboard milieu about a hundred years after a nuclear war, where a sort of neo-Puritanism has descended on the survivors...and along this line, M.K. Wren's
A Gift Upon The Shore. Poul Anderson's
Orion Shall Rise is another romp - you can guess the premise from the title!

- set a couple of hundred years in a post apocalyptic world...and there's Patrick Tilley's old "Amtrak Wars" series, but although a lot of people seem to like it, I don't.
But if you liked
Warday, try Kim Stanley Robinson's
The Wild Shore - it's not a personal fave, but it's sort of the same idea.