The Cold War wasn't really a war per se but a decades-long struggle with the Soviets and their proxies, yet it was not and is not tagged dismissively in print news media as the "Cold War." Yet the same convention was not followed recently in the pages of the Washington Post when it comes to the Global War on Terrorism in the Washington Post.
From Dan Eggen's May 23 article, "Bush Tours Once-Squalid Latrine":
With 17,000 paratroopers assembled in formation, Bush gave a speech praising their efforts and declaring that the United States was "on our way to victory" in Iraq. He also presented awards for nine soldiers, two of them posthumously, and attended a private dedication for a memorial to the "Global War on Terrorism."
The White House and the U.S. government use the term -- sometimes referred to as the Global War on Terror -- and servicemen who fit the proper criteria may wear the Global War on Terrorism Medal and/or the Global War on Terrorism Expeditionary Medal.