In 1982, Dr. Richard P. Turco coined the phrase "nuclear winter," describing a theory that ash clouds would blanket the atmosphere after a nuclear war, blocking out the sun and plunging the world (or at least parts of it) into a dry, cold winter. Turco joined Carl Sagan (among others), publishing a study simulating nuclear winter in Science in 1983. Soviet scientists were also concerned about this possibility, as it certainly did seem plausible that ash plumes could do this (the year without a summer, anyone?).
Carl Sagan's second TV series—after Cosmos—was to be based on his concern about nuclear winter. The series was never produced, and arguments about the core science behind nuclear winter continue to rage decades later.
In the "Who Speaks for Earth" episode of Cosmos, Carl Sagan explained his concern about the global arms race and the likely outcome of a nuclear-equipped world going to war. He made the key point that all the conventional bombs dropped in World War II (roughly two megatons) equal a single thermonuclear bomb—a single bomb in the next war would equal the entire previous war. The consequences are staggering. Here are two relevant clips from that episode:
In this Retro Report video, The New York Times explores the science of the "nuclear winter" theory and how our thinking about it has changed over the years. Listen up, and keep an ear out for this quote summing up the Cold War:
"Imagine a room awash in gasoline. And there are two implacable enemies in that room. One of them has 9,000 matches. The other has 7,000 matches. Each of them is concerned about who's ahead, who's stronger. Well, that's the kind of situation we are actually in." -Carl Sagan (ABC News Viewpoint, "The Day After," November 20, 1983)
The NYT has a nice write-up to go along with their Retro Report video.
If you want to go even deeper into the historical nuclear rabbit hole that exists on YouTube, check out the recording of Spacebridge, a conference linking scientists in the Soviet Union and United States. Here's the first bit (including some of the Sagan footage seen in the Retro Report above):