Skinner was born in Litchfield, Connecticut. He completed preparatory studies and graduated from Litchfield Law School, and was admitted to the bar in 1800, beginning a practice in Manchester, Vermont. In 1801, he became the state attorney for Bennington County, a position he held until 1813.

From 1805 to 1813, Skinner was a probate judge for the Manchester district; in the 1812 elections, he was elected as a Republican to the U.S. House of Representatives for Vermont's new created 5th District. Skinner served a single two-year term (the 13th Congress) from March 4, 1813, to March 3, 1815. Skinner lost in the 1814 election to the 14th Congress (to the famous paleontologist Othniel Charles Marsh) and returned to Vermont to resume the practice of law.

Skinner became an Assistant Judge on the Vermont Supreme Court in 1815 and 1816, but declined the office of Chief Justice in 1817. He was a member of the Vermont House of Representatives in 1815 and 1818, serving as Speaker in the latter year.

In 1819, Skinner briefly returned to his former position of Bennington County state attorney. The same year, he was elected Governor of Vermont, and served from 1820 until 1823, when he became the Chief Justice on the Vermont Supreme Court. Skinner held this position until 1828, when he retired from public life.

Skinner was interested in public education and served as president of the northeastern branch of the American Educational Society, and was also was a trustee of Middlebury College. He died in Manchester and was interred in Dellwood Cemetery.

Preceded by: New office U.S. Representative Fifth District of Vermont 1813-1815 Succeeded by: Charles Marsh Preceded by: Jonas Galusha Governor of Vermont 1820-1823 Succeeded by: Cornelius P. Van Ness