Culberson County was formed in 1912 from El Paso County, so if you're  searching for your ancestors before 1912, look for the census records for El Paso County.

Texas Census County Formation Maps from segenealogy.com  Shows by Census year the changes in county boundries.

Residents of Texas
1782-1836

Rootsweb Guide to Census Records plus Soundexes, Indexes and Finding Aids

Shirley Hornbeck's This and That Genealogy Tips on the Census

 #1, #2, #3

1860 Census

1860 Census for El Paso County from the El Paso TXGenWeb site

1870 Census

1870 Census for El Paso County - a work in progress - from the El Paso TXGenWeb site

1880 Census

Search the 1880 census at  familysearch.org  Select 1880 US, then Texas and El Paso County

1930 Census