He was a veteran of
World War I, and after the war, Nelson served as a lieutenant in the artillery reserve corps. In 1926 he ran and won the single
Arizona State Senate seat from
Navajo County. In 1928 he ran for re-election, and was opposed in the Democrat primary by
Robert L. Moore, a former state senator. No Republican ran for the seat, so Nelson was unopposed in the general election. 1930 saw him run again for the Senate, and was unopposed in both the primary and general elections. In 1932, Nelson decided to run for the
Arizona House of Representatives, but was defeated in general election by incumbent Republican
Charles J. McQuillan. In 1934, he attempted to return to the State Senate, and was in a three-way race in the Democrat primary, which included incumbent
Frank M. Siegmund, who had replaced Nelson in the prior legislature. Nelson was the winner of the primary, and then defeated the
Socialist Party candidate by a 20–1 margin in the general election. He decided not to run in 1936, clearing the way for Robert L. Moore to return to the State Senate. He attempted one more run for the State Senate, in 1940, but lost in the Democrat primary to
Lloyd Henning, 1,790 to 1,098. ==References==