In Ohio, the exception for CCW holders under the Improper Handling of Firearms in a Motor Vehicle Statute, which is Ohio Revised Code Section 2923.16, only applies to handguns. Given that, all long guns must be transported according to the statute.
The statute says:
No person shall knowingly transport or have a firearm in a motor vehicle, unless the person may lawfully possess that firearm under applicable law of this state or the United States, the firearm is unloaded, and the firearm is carried in one of the following ways:
- (1) In a closed package, box, or case;
- (2) In a compartment that can be reached only by leaving the vehicle;
- (3) In plain sight and secured in a rack or holder made for the purpose;
- (4) If the firearm is at least twenty-four inches in overall length as measured from the muzzle to the part of the stock furthest from the muzzle and if the barrel is at least eighteen inches in length, either in plain sight with the action open or the weapon stripped, or, if the firearm is of a type on which the action will not stay open or which cannot easily be stripped, in plain sight.
So as long as the gun is unloaded and is transported in one of those 4 ways, you should be fine.