 Nyora kupfuurira kweiyi ndima - Horowitz akanga ari mutambi anotungamirira muU.S. mukati mema1930 nama1940. Akanga ari U.S. Open Champion muna 1936, 1938, uye 1943. Muna 1941, akarasikirwa nomutambo 0313 naSamuel Reshevsky nokuda kweU.S. Chess Championship. Akatamba muU.S. Team muOlympiads ina dzeChess, muna 1931Muna 1945, Horowitz akahwina mumwe wemakwikwi maviri chete eU.S. nekukunda GM Salo Flohr. Akagovana mini-match yake yemitambo miviri achipesana naFlohr, uye muchinyorwa cha1946 chechiitiko chimwe chete, akagovana mini-match yake achipesana naIsaac Boleslavsky. 