AEP has a number of properties around the state for which you can get free camping/hunting/fishing/etc. permits. The website has a pdf file you can print and sign and you are set. Some of the camp sites (not sure which ones, tbh) are close during winter, but if you call AEP during business hours, they can hook you up with someone in corporate communications to get the details.
I've hunted (a *long* time ago) a bit on the property they have southeast of Zanesville. It was nice, big and not super crowded - fwiw.