Welcome to OCDO.
Always do your own research and do not take the word of an instructor, LEO or random guy off the internet. You are responsible for your actions.
Most instructors in my limited experience, do not like open carry because a permit/licence/permission slip is not needed to carry in Ohio under most situations. Taking advise from law enforcement is not advisable. Law enforcement can and will lie, this also applies to people on the internet.
If you are carrying on private property the property owner or agent of sets the rules. If you are in a store and they ask you to leave you must do so or you will be charged with trespass. In Ohio no gun signs have force of law so its best to avoid going into places that are posted armed.
If you have a Concealed Handgun Licence you can still open carry. Getting a CHL does not void any rights you had before you had a CHL. This is the same as a drivers licence, just because you have a drivers licence doesn't void your right to walk. In Ohio I recommend you get a CHL because the state says any loaded firearm in a vehicle is concealed regardless if you can see it or not.
Remember to look up the laws your self. Don't rely on law enforcement, instructors, or people on the net for all your information.