“The Wall” by Peter Sis and “The Loud Silence of Francine Green” by Karen Cushman are good ones if you don’t mind historical novels aimed at kids. Animal Farm is a good primer for family discussions of ideology, freedom and totalitarianism. There are some really good web pages on they Cold War aimed at kids. Without knowing the ages and/or reading levels of your kids, it’s hard to make recommendations.
Would “On The Beach” be too depressing? I spent my elementary youth doing the periodic “duck and cover” drills under our desks from kindergarden onwards and from about that age we knew (living right behind a Nike installation) that we were toast when the inevitable war with the Godless commies broke out.
Never wrestle with a pig. You both get muddy and the pig just likes it.