A native of Brooklyn, New York, who grew up in New Jersey, Snow graduated from the United States Military Academy in 1890 and commenced a long career in the Army's field artillery branch.

[3][2] His classmates included Colden Ruggles, Fred W. Sladen, Frank M. Caldwell, Clint C. Hearn, Daniel W. Ketcham, Edgar Jadwin, Francis Marshall, Harry H. Bandholtz, Henry D. Todd Jr., William C. Davis, George G. Gatley, William S. McNair and Herbert Deakyne.

[1] In 1910, Snow was assigned to the Militia Bureau as senior inspector and instructor of National Guard artillery units.

[1] In April 1917, the same month of the American entry into World War I, Snow was assigned to command the 4th Field Artillery Regiment, which he led during training at Fort Bliss, Texas, and at a temporary camp in Syracuse, New York.

[3] in July 1917, Snow was selected to command the Field Artillery School at Fort Sill, Oklahoma, and promoted to brigadier general.

[3] While at the school, Snow began the process of reorganizing it and modernizing the program of instruction to meet the increased demand created by the war.

[3] In this role, he created a system of training centers and replacement depots, which enabled the artillery branch to meet the wartime demand for qualified artillerymen.

[1] He served until retiring in 1927, and oversaw the artillery branch's postwar reorganization, including the beginning of testing and experimentation to determine how to transition from horse drawn equipment to mechanized, and modernize processes for directing and controlling indirect fire to improve speed and accuracy.

[1] The citation for his Army DSM reads: The President of the United States of America, authorized by Act of Congress, July 9, 1918, takes pleasure in presenting the Army Distinguished Service Medal to Major General William Josiah Snow, United States Army, for exceptionally meritorious and distinguished services to the Government of the United States, in a duty of great responsibility during World War I, in planning and executing those measures responsible for the efficiency of the Field Artillery during the war.

Snow was a World War I veteran who attained the rank of lieutenant colonel as an engineer officer, and was a recipient of the Distinguished Service Cross and other decorations to recognize his wartime heroism.

Snow II (1923–2011) was a 1945 graduate of West Point and a veteran of the United States Air Force who went on to a career as an Episcopal clergyman.