Nuclear Weapons in the Cold War?

I feel like one of the truisms about the reason for the relative stabil of the cold war is the advent of nuclear weapons. We certainly have never had a multipolar geo political era where nuclear weapons were around, or where there was any technology that was even analogous in a similar way. Do you think that nuclear weapons limit the extent to which petition and a nd violence can happen in this multi polar ara? I would hope that they still exert the same deterrent component that they did in the cold war.