I think we are far from it, the tension in the mid 1980s was palpable in Western Europe, many of us expected the Soviets to move between 1984 and 1986, and that would have been the end of the world as we know it.
There was really only two times when war between Russia and the US was ever close during the cold war. First at Cuba with the missiles and then when the computer error led to a launch warning. Sure it seemed like things were much closer but not really.
IMO we are far far closer to a world war then at any time since Ferdinand was shot.