Arkansas features plenty of trail systems and ATV parks for riding. Anywhere that offers OHV trails, such as Ouachita National Forest, Daisy State Park, and the Ozark Creek National Forest all feature trails that are perfect for ATV riding. Just beware that some trails are multi-use, meaning you will be sharing them with mountain bikers, horseback riders, and hikers.
Check out these Hunter, AR ATV/OHV resources: