Welcome to Alabama! I understand that Decatur has a large Tennessee Walking Horse Show every year. I'm sure people there could help you with info.
Yes, there is nice riding here. I'm also thinking that many of our state parks have good riding trails.
Actually it is the Racking Horse Celebration that is in Decatur (Priceville) It is in September I believe, is that right Frog? The Tennessee Walking Horse Celebration is in Shelbyville, TN, not to far north into TN. Both are great to attend.
Weeell, they WOULD be good riding trails, but you can't ride horses in Alabama State Parks, that I know of, and you can only ride horses on designated horse trails in the National Forests (like Bankhead and Talladega NF). We aren't exactly the most horse-friendly state I've ever heard of. :o(
There's quite a few privately owned horse camps around here though.