According to the U.S. Census Bureau, the county has a total area of 2,537 km² (980 mi²). 2,534 km² (978 mi²) of it is land and 3 km² (1 mi²) of it is water. The total area is 0.13% water.
As of the census2 of 2000, there are 4,631 people, 1,728 households, and 1,252 families residing in the county. The population density is 2/km² (5/mi²). There are 1,968 housing units at an average density of 1/km² (2/mi²). The racial makeup of the county is 91.10% White, 0.39% Black or African American, 0.54% Native American, 0.22% Asian, 0.00% Pacific Islander, 6.24% from other races, and 1.51% from two or more races. 10.90% of the population are Hispanic or Latino of any race.
There are 1,728 households out of which 36.40% have children under the age of 18 living with them, 64.70% are married couples living together, 4.90% have a female householder with no husband present, and 27.50% are non-families. 25.60% of all households are made up of individuals and 13.60% have someone living alone who is 65 years of age or older. The average household size is 2.61 and the average family size is 3.16.
In the county the population is spread out with 29.50% under the age of 18, 6.90% from 18 to 24, 26.50% from 25 to 44, 19.20% from 45 to 64, and 17.90% who are 65 years of age or older. The median age is 36 years. For every 100 females there are 98.20 males. For every 100 females age 18 and over, there are 95.00 males.
The median income for a household in the county is $36,761, and the median income for a family is $41,550. Males have a median income of $29,295 versus $20,153 for females. The per capita income for the county is $16,824. 9.30% of the population and 6.70% of families are below the poverty line. Out of the total people living in poverty, 11.90% are under the age of 18 and 5.70% are 65 or older.