The term "cold war" was used by the American State Department to refer to the rising tensions with the Soviet Union as early as 1947. Interestingly, I think, in 1947, several commentators in the State Department (here is one example) referred to the escalating tensions as the "so-called 'cold war, with the U.S.S.R.'" Some commentators continued to use quotation marks in early 1948, but by the end of that year the term had become so ubiquitous within the American political, diplomatic, and military lexicons that the habit had become pointless.

I am personally less interested in “discovering” who “coined” the term. Popular history holds that financier and presidential adviser Bernard Baruch coined the term in speech in South Carolina in April of 1947, but others have noted that his speechwriter Herbert Swope had used the term previously. Moreover, the term “cold war” had been used in at least one other context between the end of the Second World War and the rise of the Cold War. George Orwell used the term in his essay “You and the Atomic Bomb,” published after the defeat of Japan in 1945, where he warned that nuclear weapons could lead to a “cold war” (he used quotation marks) in which the state could suspend existing rights of man (note that despite the fact that the more famous Orwell used the term prior to Baruch, we cannot say he coined the term, in part because he referenced someone else’s theory, and in part because he does not use the term to refer specifically to Soviet-American relations. This underscores my point—who cares who “coined” the term!).

In any case, by the end of 1947, the term had become standard in America for referring to the geopolitical competition between the United States and the Soviet Union.