In 1880 census for California, Tulare County, Mussel Slough Twsp. Nathan T. Woodcock is single age 51 (1829) b. TN, parents TN; living in the household of an Arnett R. Woodcock age 49 (1832) b. TN parents TN. They are probably brothers.
If you are looking for an obituary also try Kings County as the 1880 Mussel Slough Twsp was located in the area of Tulare County that was "taken" as of 1893 to form Kings County-also, I believe, the county seat of Hanford is the Mussel Slough area of 1880.
1900 census there are no Woodcock families in Tulare County and one Martha Woodcock born in Oregon in Kings County. Fresno County also had land that was taken for Kings Co and there are Woodcock families in that 1900 census.
Do an internet search for the "Mussel Slough Tragedy" and you will find sources with a history of the area. The incident happened May 10, 1880 and the page of the census the Woodcock family is on was taken June 15th and 16.