Although Winston Churchill was Prime Minister of England for 4 years (1951-1955) during the Cold War, his main contribution to the Cold War comes from a time when he was not Prime Minister.
As Prime Minister, Churchill did play a role in the Cold War. Most notably, he pushed for Britain to develop its own atomic bomb. After that, he authorized development of a hydrogen bomb (a much stronger sort of nuclear weapon). By doing these things, he participated in the arms race aspect of the Cold War.
However, Churchill is best known for things he did while he was not in office. He pushed the US to take a more aggressive stance towards the Soviet Union in the period right after World War II. Most famously, he gave his “Iron Curtain” speech in early 1946. In this speech, he argued that the Soviet Union was creating an “iron curtain” that was walling off Eastern Europe into a communist bloc where there would be very little in the way of human rights. This helped to move American public opinion towards a more anti-Soviet stance.