Cold war is a state where two or more parties are not involved in direct or declared fight/war but involved in indirect fight or sabotage etc. It can happen between two countries, two people or two groups of people.
In history Cold War is a state of geopolitical tension after World War II between Soviet Union along with its satellite states and United States along with its NATO allies. Timeframe is the period between 1947 and 1991, the year the Soviet Union collapsed.