As of the census of 2000, there were 4,576 people, 1,844 households, and 1,252 families residing in the county. The population density was 6 people per square mile (2/km²). There were 2,562 housing units at an average density of 3 per square mile (1/km²). The racial makeup of the county was 92.59% White, 0.09% Black or African American, 6.32% Native American, 0.09% Asian, 0.22% from other races, and 0.70% from two or more races. 0.76% of the population were Hispanic or Latino of any race.
There were 1,844 households out of which 29.80% had children under the age of 18 living with them, 57.20% were married couples living together, 6.50% had a female householder with no husband present, and 32.10% were non-families. 30.10% of all households were made up of individuals and 16.10% had someone living alone who was 65 years of age or older. The average household size was 2.43 and the average family size was 3.04.
In the county, the population was spread out with 27.00% under the age of 18, 5.10% from 18 to 24, 22.80% from 25 to 44, 23.80% from 45 to 64, and 21.30% who were 65 years of age or older. The median age was 42 years. For every 100 females there were 100.00 males. For every 100 females age 18 and over, there were 96.80 males.
The median income for a household in the county was $30,567, and the median income for a family was $36,295. Males had a median income of $27,241 versus $17,872 for females. The per capita income for the county was $15,462. About 10.40% of families and 13.90% of the population were below the poverty line, including 19.00% of those under age 18 and 14.00% of those age 65 or over.