The line between history, journalism, and politics can be fine, but I would consider this more of a historical question than a political one at this point.
Nobody really gets that passionate about foreign policy in the Eisenhower administration anymore, even if it was a pretty hot issue back in 1960.
I would argue there are at least two cold wars from a historical perspective, and I could make a case for three (and plus two more recent ones proceeding now).
Cold War Zero between 1917 and 1933. The stated policy of the United States and many of the other Western powers after the October Revolution was to simply not recognize Lenin and the Bolsheviks as the legitimate rulers of what used to be the Russian Empire and then the Russian Republic. This included supporting the White side in the Russian Civil War, diplomatic isolation and trade embargoes after Red victory, and attempts at subversion in Russia by Western intelligence agencies and support for various international and national communist and anti-colonial movements by Lenin and Stalin. Passions eventually cooled and everybody kind of gave up on the idea of Russia going back to the old ways by the 1930s, and FDR recognized the Soviet Union as a legitimate country in 1933.
There was a definite rapprochement between the West and the Soviet Union in the 1930s, despite the various horrors of Stalinism perpetuated at the time, culminating in renewed trade, Lend-Lease, the alliance against the Germans, and allowing the Soviet Union a veto on the U.N. Security Council at the San Francisco Conference.
The First Cold War is the "classic" period of the Cold War of Dr. Strangelove, North by Northwest, and Fail Safe fame. It runs from roughly 1945 through the early 1970s and climaxes with the Cuban Missile Crisis and the Space Race.
After competing with each other on virtually every economic, military, and political front almost gets everybody killed with the whole Cuba thing and the cost of all this starts to break Washington and Moscow's backs, both sides eventually cool off, start respecting each other's right to exist, and begin some collaborative projects related to scientific and engineering research and restart of trade. Historians usually call this era of a more peaceful relationship détente, and it runs through the U.S. presidential election of 1980.
Then we have the Second Cold War after the Soviet invasion of Afghanistan, the Reagan defense buildup, and more aggressive measures by both sides to support allies throughout the world (e.g., American help for Afghan insurgents, Soviet and Cuban troops in Africa, etc.) before that ends because of the collapse of the Soviet Union and another period of general cooling. The Americans/the West really did win that one.
Then you know how it goes -- the end of history, Russian finally joining the West once and for all, maybe even eventually being invited into NATO.
Then that all kind of went away.
The historian in me wants to call our current relationship with Russia the Third Cold War. We have clearly restarted the geopolitical and ideological competition that marked the first two... or three, depending... of them in the last century. I would argue we are in one with mainland China just as much, and that really the main one right now.
So historically...
0 = tie
1 = tie
2 = clear American/Western victory
3 = ongoing
new 1 with China = ongoing
1-0-2 with two counts still with the jury