Can a non violent/non drug felon hunt in Ohio with a Muzzleloader.

Such a person can probably buy a hunting license. I believe what you are asking is whether he or she can legally possess and carry a muzzle-loading long gun.

It might not be a violation of the Federal Firearms Act - there is an exception for muzzleloaders designed or manufactured before 1898. So that would depend upon whether the weapon was designed after that year.

Whether the State of Ohio has further restrictions, however, is something else. Ohio Revised Code 223.14 only applies to persons convicted of a "violent" felony, or involved in illegal drug abuse, so it apparently isn't a problem. http://www.atf.gov/files/publications/download/p/atf-p-5300-5-31st-editiion/States/atf-p-5300-5-ohio-2010.pdf