Born near Millersburg, Ohio, Cowen attended the public schools and the local academies at Fredericksburg and Hayesville, Ohio. He graduated from Princeton College in 1866 and from the law department of the University of Michigan at Ann Arbor.
He was admitted to the bar of Ohio in 1868 and commenced practice in Mansfield, Ohio, including service as prosecuting attorney of Holmes County. Cowen moved to Baltimore, Maryland, in February 1872 and was appointed counsel of the Baltimore and Ohio Railroad (B&O), and from 1876 to 1896 he served as the general counsel He was elected as a Democrat to the Fifty-fourth Congress, serving from March 4, 1895 to March 3, 1897, but was not a candidate for renomination in 1896 to the Fifty-fifth Congress.
In January 1896, Cowen was chosen to be president of the B&O Railroad, a position he served in until June 1901.
He died in Chicago, Illinois, and was interred in Oak Hill Cemetery in his home town of Millersburg.
Member Congress, 1885-1887, as free trader, opposed by Gorman wing of party.