In 1863 Woodman emigrated to the United States arriving in Philadelphia and immediately enlisted in the Gulf Squadron of the United States Navy. He moved to Chicago in 1865, graduating from the law department of Chicago University in 1871. He was admitted to the Illinois bar the same year and commenced practice in Chicago.
He was appointed prosecuting attorney of the lower courts in 1877 and Justice of the Peace by the judges of Cook County in 1881.
Woodman was elected as a Republican to the Fifty-fourth Congress (March 4, 1895 - March 3, 1897). He was an unsuccessful candidate for reelection in 1896 to the Fifty-fifth Congress.
He engaged in the practice of his profession until his death. He died in Elgin, Illinois, March 18, 1898.
He was interred in Rosehill Cemetery in Chicago.