So by extention could the entire Cold War be counted as World War 3? It was fought not with guns but economies.
I teach the Cold War as though it was a "real war". Divided into different phases and different theatres of operations.
Matt White's Great Big Book of Horrible Things attributes 11 MILLION deaths to the Cold War directly (and if we add such things as internal communist oppression of their own people in places like China, the death toll jumps to the 40 MILLION range at minimum).
Abeit spread over 40 years or so. That's still a million people dead each year due to the Cold War on the average.
And for what its worth, though the Cold War didn't have nuclear weapons dropping on cities, at the very least thousands of people died directly as a result of nuclear weapons. The Soviets marched thousands of soldiers directly through an irradiated area at least once with the death toll in the thousands (perhaps).
And though American/Soviet direct conflict was avoided for the most part, I've counted up anywhere from 300-500 instances of direct conflict between U.S. and Soviet forces in the air or at sea over the decades.