A Democrat, Nelson is a former mayor of Carrboro, North Carolina and the first openly gay person to be elected as a mayor of a North Carolina city. Nelson was elected in 1995 after serving two years on the Carrboro Board of Aldermen. He served five consecutive terms as mayor from 1995 to 2005. He has since moved to Hillsborough, North Carolina.
In November 2006, Nelson was elected to the Orange County Board of Commissioners. In 2007, he announced his intention to run for the North Carolina Senate in 2008, seeking to replace retiring Sen. Ellie Kinnaird in the reliably-Democratic 23rd district, which contains Orange and Person counties. When Kinnaird changed her mind and decided to run for re-election, Nelson suspended his own campaign.