Some of the Ouachita National Forest in SE Oklahoma has overnight backpacking areas. The "Black Fork Mountain Wilderness" is both in Oklahoma and Arkansas. The rules state "Camp and Travel on Durable Surfaces", so you can hike until you find your spot and then camp.
Here's a link that shows five areas that allow that over-night backpacking.
https://stepoutside.org/article/5-beautiful-backpack-camping-spots-in-oklahoma/
Here's a link that shows five areas that allow that over-night backpacking.
https://stepoutside.org/article/5-beautiful-backpack-camping-spots-in-oklahoma/