Here is a Arkansas 4x4 site, I didn't look into it with much detail but from what I have heard there are some places out there.
http://arkansascrawlers.com/yabb/YaB...rd=Trail_Rides
http://www.ozark4x4.com/ - and Ozark
You can check it out for close trails. Since you haven't much experience, you will have to be careful about your fist ventures and do what is comfortable for you.