Born in Cazenovia, New York, Cole attended the common schools and was graduated from Union College, Schenectady, New York, in 1843. He studied law. He was admitted to the bar in 1845 and commenced practice in Chicago, Illinois. He moved to Potosi, Wisconsin, the same year and continued the practice of law. He served as member of the State constitutional convention in 1847.
Cole was elected as a Whig to the Thirty-first Congress (March 4, 1849 - March 3, 1851). He was an unsuccessful candidate for reelection in 1850 to the Thirty-second Congress. He resumed the practice of law in Potosi until 1855. He served as associate justice of the State supreme court 1855-1880, and chief justice from April 1881 to January 4, 1892. He resumed the practice of law. He retired in Milwaukee, Wisconsin, where he died on May 5, 1903. He was interred in Forest Hill Cemetery, in Madison, Wisconsin.