He received limited schooling, and removed to Bath in 1813.
Then he studied law, was admitted to the bar and practiced in Bath.
He was a member of the New York State Assembly in 1823 and 1828.
Woods was elected as an Adams-Clay Democratic-Republican to the 18th United States Congress to fill the vacancy caused by the resignation of William B. Rochester and served from December 1, 1823, to March 3, 1825.
He was buried at the Grove Cemetery in Bath.