People grossly, grossly overestimate the long-term effects of fallout. The main negative effects of nuclear warfare would be infrastructure destruction and the collapse of food/medicine distribution - fallout wouldn't even register.
At the height of the Cold War, a full-on strategic exchange between the US and the USSR wouldn't have ended human civilization. Things would've been unpleasant in parts of North America and Eurasia for a time, but all these extreme scenarios that are sensationalized wouldn'tve come to pass.
Look at Chernobyl - it's essentially a thriving wildlife reservation, now.