Sponsored Topics. Carrizozo is a town in and the county seat of Lincoln County, New Mexico, United States. The population was 1,036 at the 2000 census. Carrizozo is located at 33°38′38″N 105°52′39″W / 33.64389°N 105.8775°W / 33.64389; -105.8775 (33.643946, -105.877435).