How did nuclear warfare affect the cold war?

That refers to warfare that includes nuclear weapons, also known as atom bombs.

The only country to have used nuclear warfare in history is the USA

There has not been nuclear warfare. There have been two nuclear attacks.

Nuclear warfare denotes the use of nuclear weapons by both or all opposing sides. The only use of nuclear weapons in warfare were the two bombings by the US of Hiroshima and Nagasaki, and it was the intent of the US to bring WW2 with Japan to a quicker conclusion.

Arthur Katz has written:

'The social and economic effects of nuclear war' -- subject(s): Economic aspects of Nuclear warfare, Nuclear warfare, Social aspects of Nuclear warfare