We have caamped several times at Beavers Bend SP and enjoyed it alot. If you call prior to departure, they will (generally) tell you if they are busy or not. We have stayed in several of the SP's the week after Christmas and have never found a full park.
On the off chance that they are full, you can go over to Hochatown SP (same lake) and should be able to pick a spot! We drive up from East Texas and have never found a full park. It is first come first serve, and we enjoy the bluff area at Beavers Bend best.