Either, really. The US never really shook off it's commitment to massive retaliation, as NATO was operating from a position of inferiority in conventional arms prior to the mid-80s. The Soviets, in the meantime, initially regarded nukes as a regular part of warfare but then about faced in the course of the middle of the Cold War into utilizing their nukes to assist and safeguard their conventional superiority. This came with the caveat that they were willing to pre-empt NATO attempts use of nuclear weapons to reverse battlefield defeats by using them first. And then there are the French, who built their nuclear arsenal as a means to make damn sure that the US would have no choice but to follow through on it's nuclear umbrella, since they understood that if they started nuking the Russians, the Russians would start nuking not only them but the US as well.
The Chinese under Mao were also quite unpredictable. Mao constantly talked about China's sheer population being able to absorb nuclear strikes and the bomb as a mechanism of finishing the revolution. He even had a "people's bomb" designed, intending to use it as an export to other developing communist countries, so it wasn't all just talk. Up until the North Koreans got the bomb (and it's arguable even then), he was probably the most dangerous national leader to ever acquire nuclear weapons.
Not after the mid-60s, they wouldn't have.