There are a couple of state run ranges within an hour of Batesville, and Haspin Acres, a private off road park for riding 4 wheelers is 30 minutes away. There are 10 public campgrounds within 60 miles. So, there are a lot of places to go. It is not, however, like you are used to. No great expanses of land to do whatever you want, most of the state is private farm land, but we try to scatter as many public places around as we can.
The weather is very diverse. It can get in the 90's in the summer, and 20 degrees and snow in the winter. If you don't mind cold, you can camp all year, but I stop in October usually. If you Google map Batesville, and zoom out, you can see the green areas of public land that are close. Lots of fishing and hiking. The 4 wheelers are a no go on most state park land, but you can find private places to ride pretty easy.
As small as Batesville is, it shouldn't be too hard to make friends with a local farmer or two, and get invited to hunt and or shoot on someones farm.
You picked a good area. It's small enough to have that know your neighbors small town feel, and yet you can almost see Cincy from there. I think your going to like it there.