Who was the last classical musician to appear on the cover of Time? According to the magazine's website (if a search for "music" on the covers page does not lie), it was Vladimir Horowitz, in 1986. The last living composer to appear on the cover (excluding the polymath Bernstein)? Stravinsky, in 1948. Only one all-classical American composer has ever been chosen for the signal honor: Deems Taylor, in 1931. Among conductors, Toscanini appeared three times, Stokowski and Koussevitzky twice, and Beecham, Szell, Zubin Mehta, and James Levine (in 1983) once. Among composers, Richard Strauss appeared twice, Sibelius, Shostakovich, Mascagni, Britten, Stravinsky, and Johann Sebastian Bach once.
Addendum: I missed Gian-Carlo Menotti in 1950.