As of the census of 2000, 3,966 people, 1,058 households, and 757 families resided in the county. The population density was 4 people per square mile (2/km²). There were 1,488 housing units at an average density of 2 per square mile (1/km²). The racial makeup of the county was 88.20% White, 0.98% Black or African American, 0.48% Native American, 0.08% Asian, 0.10% Pacific Islander, 8.93% from other races, and 1.24% from two or more races. About 41.33% of the population were Hispanics or Latinos of any race.
Of the 1,058 households, 29.80% had children under the age of 18 living with them, 59.40% were married couples living together, 9.70% had a female householder with no husband present, and 28.40% were not families. About 26.60% of all households were made up of individuals and 14.20% had someone living alone who was 65 years of age or older. The average household size was 2.45 and the average family size was 2.97.
In the county, the population was distributed as 16.10% under the age of 18, 10.40% from 18 to 24, 38.20% from 25 to 44, 21.50% from 45 to 64, and 13.80% who were 65 years of age or older. The median age was 36 years. For every 100 females, there were 181.30 males. For every 100 females age 18 and over, there were 209.90 males.
The median income for a household in the county was $31,313, and for a family was $36,894. Males had a median income of $20,750 versus $21,458 for females. The per capita income for the county was $15,727. About 7.50% of families and 11.90% of the population were below the poverty line, including 15.80% of those under age 18 and 14.20% of those age 65 or over.