Stedman first got involved in politics as a delegate to the 1880 Democratic National Convention, which nominated Winfield Scott Hancock and William Hayden English for President and Vice President of the United States. He was elected the fifth Lieutenant Governor of North Carolina in 1884, serving from 1885 to 1889, and unsuccessfully ran for the Democratic nomination for Governor of North Carolina in 1888. He moved to Asheville, North Carolina in 1891 and to Greensboro, North Carolina in 1898, continuing to practice law. Stedman served as a trustee of the University of North Carolina from 1899 to 1915, was president of the North Carolina Bar Association from 1900 to 1901, was again an unsuccessful candidate for Governor of North Carolina in 1903-04, and was director and president of the North Carolina Railroad from 1909 to 1910.