There is one park in Louisiana. Its near Sicily Island, LA not far from Natchez, MS. Its called AREA2 at Catahoula Recreation. The website is www.atvdirtbikerecreation.com
We've been building trails out there for Dennis over the last couple of years. Its coming along nicely.
If you want to hook up with Louisiana wheelers on private land (legal only), go to www.louisianaoffroaders.com
Several clubs post their rides on there, including the one I'm President of - Louisiana 4x4.
We have stock rigs out with us to the wild/extreme. So, no fear if its your first time. Usually have about 4 or so new folks out with us each time. Pretty much the same for the other local clubs as well.
Good luck, hope to see you on the trail.