Winston Churchill did not invent the iron curtain. He made it famous, which is a different thing.
The phrase began in the theatre. A June 1794 item in the Monthly Review described an "iron-curtain" at the new Drury Lane theatre. It was a barrier meant to shield the audience if a fire broke out on stage. By 1819 English speakers were using it figuratively for any impenetrable barrier.
The political use came about a century later. In 1917 and 1918 the Russian writer Vasily Rozanov wrote, in installments of The Apocalypse of Our Time, that an iron curtain was coming down on Russian history. The International Churchill Society counts that as the phrase's first appearance in print in this political setting. In 1920 Ethel Snowden used the phrase for the Soviet border in her book Through Bolshevik Russia.
Then German propagandists took it up. In May 1943 the magazine Signal wrote of an iron curtain separating the world from the Soviet Union. On 25 February 1945 Joseph Goebbels warned in Das Reich that an iron curtain would fall over the territory the Soviets controlled if Germany lost. Etymonline notes that he used the German form, ein eiserner Vorhang.
Churchill's first recorded use came in a message to President Truman on 12 May 1945, warning that an iron curtain had been drawn down across the Soviet front. Accounts differ on whether it was a telegram or a letter. Allen Dulles used the phrase at a Council on Foreign Relations meeting on 3 December 1945, before the famous speech.
That speech came on 5 March 1946 at Westminster College in Fulton, Missouri. Churchill said: "From Stettin in the Baltic to Trieste in the Adriatic, an iron curtain has descended across the Continent." The phrase became the standard name for the division of Europe.
It also became a template. "Bamboo curtain" appeared by 1947, first for French censorship in Indochina, and by 1949 for communist China. It was evidently modeled on the older phrase.
New earlier uses keep turning up, so "earliest known" is the safest wording. What is settled is that the phrase was already in circulation, and that the Fulton speech is why we remember it.