Osborne was a free silver supporter and during the 1896, 1900, and 1908 presidential elections he supported William Jennings Bryan. In 1896 he served as chairman of the Wyoming delegation to the Democratic National Convention, in 1898 he served as vice chairman of the Democratic National Committee, was made a member of the national committee in 1900, and served as the vice chairman of the finance committee in 1908. During the 1904 presidential election Bryan suggested that somebody like Osborne from the western United States should run for the Democratic nomination, but Osborne chose not to run.