Cox apprenticed with his father, who he worked with when working on murals for the
Wisconsin State Capitol. His first solo mural may have been over the fireplace at the Windsor Public Library. Like his father, he served as the president of the
National Society of Mural Painters. In 1953, he was hired to complete the
frieze in the Capitol Rotunda, which had been originally started by
Constantino Brumidi and left unfinished since the 1880s. He painted murals on many other walls in the building, including a depiction of the
first landing on the Moon in the Senate's
Brumidi Corridors of the Capitol. Starting in 1971, Cox designed and painted two of the three Cox Corridors in the Capitol, while the third was completed following his designs after his death. Some of his work may be seen at the
George Washington Masonic National Memorial in
Alexandria, Virginia. He also painted murals in houses owned by Anne (Mrs. William K.) Vanderbilt and Lincoln Ellsworth. In 1956, he was hired to design and paint two long rectangular murals for the new headquarters of the
North Carolina Grand Lodge of Ancient, Free and Accepted Masons. The murals depict major events in the history of North Carolina Masons from the 1750s onward. These were completed in August 1959, transported to the building, unrolled, and mounted to the north and south walls of the main hall. He served as president of the
National Society of Mural Painters from 1942 to 1946 and again from 1960 to 1963. ==Personal life==