The Cold War was a global struggle, but should not be considered a war. There was a constant threat of war throughout the period, but the US never fell to direct conflict with the main aggressor, Russia. This period can be eloquently described by the words of French Sociologist and political expert, Raymond Aron; ‘impossible peace, improbable war.”  The government even references the Cold War as "arguing on the world stage that Western-style democracy was superior". The US's involvement in the Cold War can be boiled down to an ideological disagreement and nothing more.
The US has not officially declared war since WW2 despite being active in conflicts, primarily due to the fact that by remaining formally neutral, less responsibility falls on members of the US government.  Therefore, an official declaration or documented conflict should not be needed to define a war.