Born September 2, 1817 near Columbia, Kentucky, Wolford attended the common schools. He studied law. He was admitted to the bar and commenced practice in Liberty, Kentucky. He served as member of the State house of representatives in 1847, 1848, 1865, and 1866. During the Civil War served as colonel of the 1st Kentucky Cavalry, 1861-1864. He served as adjutant general of the State of Kentucky in 1867 and 1868.
Wolford was elected as a Democrat to the Forty-eighth and Forty-ninth Congresses (March 4, 1883 – March 3, 1887). He was an unsuccessful candidate for reelection in 1886 to the Fiftieth Congress. He continued the practice of law in Columbia, Kentucky, until his death there August 2, 1895. He was interred in Columbia Cemetery.