I lived at one of the points that could be considered the height of the Cold War and I would definitely say that I feel safer today than I did back then. I think this is even more true if we go back to the times that my parents lived through.
I was in high school and college in the Reagan years. This was one time when the Cold War seemed to be at something of a time of high tension. It was not as bad as the time of the Cuban Missile Crisis, perhaps, but there was a great deal of worry about global nuclear war. Many movies, for example, were made about nuclear war and its aftermath (like the Mad Max movies or “The Day After”). There were songs sung (like “Russians” by Sting) about the possibility of nuclear annihilation.
Today, it is clearly possible to worry about the global situation. It is possible that further terrorist attacks will be launched against the US. It is possible that China will come to challenge the US as a superpower. However, at the moment, none of these things has the potential to destroy the world in the way that the Cold War could have at its height.