Mountain Park is a town in Kiowa County, Oklahoma, United States. The population was 320 as of the 2020 United States census. The town of Mountain Park began as a trading post named Burford, near the Wichita Mountains in southern Oklahoma Territory. A post office was established at Burford in August 1901, just after the Kiowa, Comanche, and Apac…Mountain Park is a town in Kiowa County, Oklahoma, United States. The population was 320 as of the 2020 United States census. The town of Mountain Park began as a trading post named Burford, near the Wichita Mountains in southern Oklahoma Territory. A post office was established at Burford in August 1901, just after the Kiowa, Comanche, and Apache Reservation opened for settlement by non-Indians. In February 1902, the town that had sprung up around the trading post and changed its name to Mountain Park. Fires destroyed most of the wood-frame buildings along Main Street in 1906 and 1908. The town rebuilt with all brick structures.