Another possible earlier Cold War could be a three way cold war between a Napoleonic France victorious in Europe, Great Britain and the Russian Empire. Basically, Russia remains loyal to the Continental System, and Britain sues for peace, perhaps after a naval war of attrition. France and Britain would still be tense toward each other, while relations between France and Russia sour later on. That would most certainly be on a worldwide scale.
If you would want to go earlier, albeit "less worldwide", a Cold War between a more tightly knit Holy Roman Emprie and the Byzantines; a sort of west vs. east religious Cold War, in the Middle Ages.

Not sure how it could happen exactly, just thinking alloud I guess.