He was educated at private schools in Augusta, the Richmond Academy, and Shenandoah Valley Academy at Winchester, Virginia. He attended the United States Naval Academy in 1885 and 1886, and became a newspaper reporter for the New York World in 1886.
He originated the plan for the national highway from New York City to Jacksonville, Florida, and was vice chairman of the Democratic National Committee from 1932 to 1935. Cohen was appointed on April 25, 1932 to the United States Senate as a Democrat to fill the vacancy caused by the death of William J. Harris and served from April 25, 1932 to January 11, 1933, when a successor was duly elected and qualified. He was not a candidate in 1932 to fill the vacancy, and continued his former business activities until his death in Atlanta.
He was buried at Westview Cemetery, in Atlanta.
He was secretary to Secretary of the Interior Hoke Smith from 1893 to 1896, and was a member of the press galleries of the United States Congress from 1893 to 1897. He was a member of the army of occupation in Cuba, and was president and editor of the Atlanta Journal from 1917 to 1935.