Born in Colton, New York, Snell graduated from the Potsdam Normal School in 1889 and from Amherst College in 1894. He began work as a bookkeeper and afterward became secretary and manager of a paper company in Potsdam, New York. In 1904 he organized the Canton Lumber Co. in Potsdam. He was president and manager of cheese manufacturing company of New York City, owner of a power plant in Higley Falls, New York, director of the Northern New York Trust Company, the Agricultural Insurance Co. of Watertown, New York, and Gould Pumps, Inc., Seneca Falls, New York. He was vice president of the Northern New York Development League, 1908-1910.

He was member of the Republican State committee 1914-1944 and delegate to all Republican National Conventions 1916-1940, serving as chairman in 1932 and 1936. Snell served as president of Clarkson College, in Potsdam, New York, 1920-1945; elected as a Republican to the Sixty-fourth Congress to fill the vacancy caused by the death of Edwin A. Merritt, Jr.; reelected to the Sixty-fifth and to the ten succeeding Congresses and served from November 2, 1915, to January 3, 1939, when he retired from politics. At various times in his Congressional career, he was chairman of the Committee on War Claims and the Committee on Rules. He served as House minority leader from 1931 until his retirement.

He was publisher of the Potsdam Courier-Freeman newspaper 1934-1949 and in 1941 became owner and manager of the New York State Oil Company, of Kansas. After his death in Potsdam, New York, in 1958, he was interred in Bayside Cemetery.