The Cold War was a war because of the Red Scare
The term “war” can be abstract, and a formal declaration of war is not needed for it to be considered a war. In the present age, the US is fighting a “war” against multiple enemies who are not entirely visible. Many nations have come out with campaigns coining the war on terror or the war on crime and these various other social issues. The war on communism was no different at the time of the cold war. The red scare faced by America is clear in the legislation of the time. For example, a foreign policy of “massive retaliation” was adopted during the Eisenhower administration to counter the threat of communist soviets and further established that America was prepared to use their tactical nuclear weapons to blunt any soviet attacks. President Harry S. Truman also signed Executive Order 9835, which created the "Federal Employees Loyalty Program". This established political loyalty review boards within federal government offices who would maintain an acceptable level of Patriotism within the workforce while also recommending termination of those who were suspected or had confessed of being "Un-American" or even worse, a Soviet spy. Although there was no formal declaration of war, the US government, through the employment of these aggressive foreign policies, was clearly instigating one. The Cold War was a war fought on a bloody ideological battleground where Western thought fought for salvation against communism.
The Cold War/War on Communism should not be equated to initiatives such as the War on Terror, considering there were direct "boots on the ground" involvement in those examples. There were none during the War on Communism.