According to the website
http://knowyourcampground.com/arkansas-state-parks/ alcohol and alcohol consumption is allowed in Arkansas State Parks and campgrounds.
As long as you don't get drunk by drinking too much alcohol or allow minors to drink any of the alcohol while in the state park then you should have no trouble bringing alcohol in the Arkansas State parks or drinking it.
Just be sure to dispose of the alcohol containers properly and do not get drunk and cause a ruckus because then you could get into trouble.
I've drank some beer before in a few Arkansas State Parks but I never drink enough beer to get drunk because I've been drunk before and it's a terrible feeling when you get that hangover after drinking too many beers.
So drink the alcohol responsibly and you should have no trouble drinking the alcohol in the Arkansas State parks or other parks that allow alcohol.