Cleburne County is a county located in the U.S. state of Arkansas. As of the 2010 census, the population was 25,970. The county seat and most populous city is Heber Springs. The county was formed on February 20, 1883 as the last of Arkansas's 75 counties to be formed. It is named for Confederate General Patrick Cleburne. Cleburne is an alcohol prohibition or dry county.