[2] Hough graduated from the University of Missouri in 1854 and read law in the office of E. L. Edwards in Jefferson City, to gain admission to the bar in 1859.

[2][3] He was in partnership with J. Proctor Knott until 1861, when he accepted the appointment of Adjutant-General of Missouri from Governor Claiborne Fox Jackson, whom he accompanied to the South.

[2] He served as Missouri Secretary of State under Governor Thomas Caute Reynolds, and on the staffs, successively, of Generals Polk, S. D. Lee, and Taylor.

After the war, he practised law in Memphis, Tennessee, until the removal of the Test Oath in 1867 permitted him to do so in Missouri.

[3] Hough died at his home in St. Louis from a brain hemorrhage following a seven-week illness.