Arthur attended and graduated from Columbia University with an A.B. in 1915. He later attended and graduated from Princeton University, and he received an honorary Doctor of Divinity from Alma White College in 1927. He married Kathleen Merrell White in 1914, and had the following children: Arlene White (1916–1990), who married Jerry Lawrence, and was a bishop at Zarephath, New Jersey; Horace White (b. 1920), who lived in California; Constance White (b. 1924); and Pauline White (b. 1927), who married Robert Barney Dallenbach, in Denver, Colorado.