Alva Hough was born on September 7, 1820, in Clove Valley, New Jersey, to Anthony Hough and Elizabeth Coon. His father was listed as a "Gentleman" in the 1850 census. Hough married Arminda Myers in Greenville, New York, in November 12, 1842, and their son Benjamin was born around 1843. In 1850, the family was living in Wantage, New Jersey, and Hough was working as a millwright. A decade later, the census listed him as a laborer, and he owned $500 of real estate and $200 of personal property.
Hough enlisted in the Union army on August 9, 1861, in Newton, New Jersey, and he mustered in as a private in Company A of the 2nd New York Cavalry later that day. The regiment spent the winter defending Washington, D.C. He mustered out on January 31, 1862, and spent the next two years at home. He returned to the army on August 20, 1864, mustering in as a private in Company F of the 124th New York Infantry. The regiment took part in the Siege of Petersburg and the Appomattox Campaign. Hough mustered out in New York City on June 16, 1865.
Hough's wife Arminda died in Wantage on October 16, 1865. He married Martha Vail in Port Jervis, New York, on February 10, 1869, and they had at least three children: Irving, born around 1870; Martha, born around 1874; and Frederick, born around 1878. In 1870, the family was living in Deerpark, New York, and Hough was working as a carpenter. He probably moved to Port Jervis sometime in the 1890s, and he died there on July 28, 1900. Martha secured a widow's pension soon afterward.