Woodcock attended the public schools, then studied law, was admitted to the bar, and practiced. In 1807, he married Mary I. Baker (ca. 1787-1860). He moved to Ithaca, and he was appointed postmaster on November 19, 1808.
He was a member of the New York State Assembly (Seneca Co.) in 1814-15. He was District Attorney of the Thirteenth District (comprising Seneca, Tompkins, Cortland and Broome counties) from 1817 to 1818; and of Tompkins County from 1818 to 1823. He was the first President of the Cayuga Steamboat Company when it was organized in 1819.
After leaving Congress Woodcock resumed the practice of law. He was President and Trustee of the Village of Ithaca in 1823, 1824, and 1826. He was again a member of the State Assembly (Tompkins Co.) in 1826.
In 1826 Woodcock was elected to the 20th United States Congress, holding office from March 4, 1827, to March 3, 1829. He took a prominent part in the Anti-Masonic movement and was a delegate to the first Anti-Masonic Party State convention, which was held in Utica in August 1828.
After leaving Congress the second time, he again resumed the practice of law. He died in 1835 and was buried at the City Cemetery in Ithaca.
His daughter Mary was married to New York Attorney General Stephen B. Cushing.
