Schueler studied at the University of Wisconsin from 1934 to 1940, earning a B.A. in economics and an M.A. in English literature. During World War II, he served as a B-17 navigator in the U.S. Air Force, stationed in England. Upon his return to the United States, Schueler began painting in Los Angeles. He studied at the California School of Fine Arts in San Francisco under Clifford Still. Throughout his career he lived and worked in New York with periods abroad, returning again and again to Mallaig, Scotland, where he and his wife lived in an old schoolhouse on the Sound of Sleat, a small fishing town which, with its surrounding scenerly, provided inspiration for the artist's paintings.
Schueler had many solo exhibitions during his career including those at the Leo Castelli Gallery, New York in 1957 and 1959; the Whitney Museum of American Art, New York, in 1975; Dorothy Rosenthal Gallery, Chicago, in 1981 and 1984; A.M. Sachs Gallery, New York in 1982 and 1984; and the Katharina Rich Perlow Gallery, New York, in 1987, 1988, and 1991. Schueler's large-scale abstractions are part of the permanent collections of the Cleveland Museum of Art, the Whitney Museum of American Art and of the Glasgow Art Gallery and Museum, Scotland, and the Scottish National Gallery of Modern Art. He was married five times; his last wife was Magda Salvesten, an art historian.