Dodd was an architectural student at the Georgia Institute of Technology for the the year of 1926-27, but in 1928 moved to New York to pursue his studies at the Art Students League, where he worked under Boardman Robinson and George Bridgman. He also studied with George Luks at this time. After a brief return to Georgia in 1930, he was again at the League in 1931, studying with John Steuart Curry and Jean Charlot. His first one-man show was presented by the Ferargil Galleries, New York, the same year.
In 1938 Dodd was appointed head of the art department of the University of Georgia, Athens, and began his life-long teaching career and association with that institution; he was the first recipient of the Dodd Professional Chair of Art, endowed by the University in his honor in 1970.
In addition to pursuing successful careers as painter and teacher, Dodd has been especially active in administrative and advisory service related to these professions. A selection of these include: president of the College Art Association of America, 1954-56; director, Carnegie Corporation of New York's Study of the Arts of the United States, 1955; charter member of the United States Advisory Commitee on the Arts, 1957; chairman of the jury of selections for Fulbright Awards in Painting, 1961-62; director, National Council of the Arts in Education, 1962. In addition he has lectured widely in America, and abroad under the auspicies of the United States Information Agency.
Among the many institutions that have awarded prizes for his paintings are: the High Museum of Art, Atlanta, Georgia; Virginia Museum of Fine Arts, Richmond; Pennsylvania Academy of the Fine Arts, Philadelphia; and from the Academy the Palmer prize in the annual exhibition of 1953.