Horowitz was a leading player in the U.S. during the 1930s and 1940s. He was U.S. Open Champion in 1936, 1938, and 1943. In 1941, he lost a match (+0−3=13) with Samuel Reshevsky for the U.S. Chess Championship. He played on the U.S. Team in four Chess Olympiads, in 1931, 1935, 1937, and 1950; the first three of which were won by the U.S. In a famous USA vs. USSR radio chess match 1945, Horowitz scored one of the only two wins for the U.S. by defeating GM Salo Flohr. He split his "mini-match" of two games against Flohr, and in the 1946 edition of the same event, split his mini-match against Isaac Boleslavsky.