Imagine, if you would, a hypothetical parallel history where during WWII Hitler or Mussolini visited the US. Imagine it's 1943 and Bing Crosby is putting on a live performance in Berlin. Imagine it's 1944 and trade between the US and Japan accounts for 1% of the total trade for both countries. These events would be patently ridiculous in the context of the global total war that was the Second World War, but comparable events happened during the Cold War. Khrushchev visited the US in the 1950s. Elton John, Billy Joel, and many many other western musical acts played behind the Iron Curtain, some in concerts in Moscow. In the 1980s the US and USSR traded directly with each other, in the late '80s the US was exporting a significant amount of grain to the Soviet Union and helping to keep the population fed. In 1975 an Apollo capsule and a Soyuz capsule met each other in orbit, the crews shook hands, exchanged gifts and so forth while the capsules stayed docked together for two days. There are a zillion other individual examples from throughout the Cold War. The point being that the "war" itself was conducted mostly behind the scenes, through proxy conflicts, diplomacy, international competition (in the space race, in the olympics, in science, in technology, in chess, etc.), and intrigue (spying, counter-spying, assassination, etc.)

It is perfectly fair to characterize the Cold War as a major event of geopolitical scale and consequence on the same footing as the world wars, but it's also not fair to pretend it was the same kind of best as those.

There are many historians who look at the Cold War in a similar way but through a different framing, often by identifying the wars as notable flare ups within a context that spans a longer period, typically the start of WWI through the end of the Cold War. The "short 20th century" as Eric Hobsbawm terms it. In my view that's probably how future historians will eventually view the contentious and conflict ridden 20th century (including the many conflicts of decolonization). As not a set of disparate events but as a continuum of conflict that flows one into the next (as in the case of the Hundred Years War or the Napoleonic Wars).