I didn't see where anyone answered your quesiton, what do they do at reenactments? If they did I simply missed it.
Ideally they attempt to recreat what ever battle occurred. They however tend to become sort of generic battles, especially those held in Indian Territory. It is near impossible to represent the Cabin Creek battles because of lack of Indian Troops, Black troops, and all the proper trappings of the soldiers who fought in the Nations. Plus it is kind of hard to represent a 500 wagon tran with one or two wagons, but having said all that a reenactment allows you to see much that you can't get in books. You can here the muskets fire, see the smoke, see the war in color much as it would have looked. Listen to reenactors tell about the living conditions and much more. By the way if you can only make one day I think saturdays are much better than sundays at most events. The reenactors start getting ready to leave before the battles and by the time it is over many simply head straight to their cars. So sat. is much better, and there is alot to see including the sutlers.