Anyhoo, Dr. Strangelove and Failsafe are the two best direct depictions of the cold war, IMO, and both awesome films.
I knew EB would recommend
Fail Safe, so I’ll just second it.
Noteworthy about that film is that in an article I read today about relations with Iran, someone commented how the US had open communications with the USSR all throughout the Cold War, even while contemplating blowing each up other up; while we have basically had no communication with Iran since 1979.
The Day After is a TV film, and has the looks and feel of one, but is a pretty intense vision of what could happen if a big one was dropped in our back yard.
There are plenty of movies about Vietnam, and even more that use Vietnam as a backdrop, even if they are not necessarily
about the war, like
Apocalypse Now and
The Deer Hunter. I would be hard-pressed to think of my top pick(s).