Adam C. Snyder was born in Crab Bottom in Highland County, Virginia on March 26, 1834 to John and Elizabeth Halderman Snyder. He prepared for undergraduate studies at the Tuscarora Academy in Juniata County, Pennsylvania and entered Dickinson College in Carlisle, Pennsylvania in September 1856 as a member of the class of 1859. Snyder enrolled at Dickinson with James J. Patterson, whose father had helped found Tuscarora. While at the College, Snyder was elected to the Belles Lettres Society, but he transferred to Washington College in Maryland in 1857 to complete his education. Snyder studied law under Judge J. W. Brokenbough in Lexington, Virginia and was admitted to the Virginia bar in 1859. He opened a practice in Lewisburg, Virginia soon after.
By 1860, Snyder was a deputy United States marshal, based in Lewisburg, and he was named prosecuting attorney for Highland County, Virginia in 1861. The Civil War intervened, and Snyder enlisted and served as adjutant in the 27th Virginia Infantry, which became a part of the "Stonewall Brigade" for the duration of the war. Snyder was wounded in the side at the first battle of Manassas/Bull Run in July 1861. He spent a significant amount of time as a prisoner in Athenaeum Prison in Wheeling, Virginia before gaining his freedom in March 1864. Following the war, Snyder returned to his office as prosecutor. He built a highly successful career in the following years, serving as a judge, as an associate justice, and then as chief justice on the West Virginia Court of Appeals between 1882 and 1890. Snyder also served as president of the bank of Lewisburg.
Snyder married Henrietta H. Cary of Lewisburg in June 1869, and the couple had nine children. Adam Snyder died in Lewisburg on July 24, 1896. He was sixty-two years old.