The .375 Winchester has been on the ODNR list of approved straight walled cartridges prior to the 2017 change that permits any straight walled cartridge of .357 caliber minimum to .50 maximum & should work just fine.

The only issue with the .375 Winchester is the limited availability of ammunition & components & rifles chambered for it. I would love to find a reasonably priced Savage 99 in .375 Winchester for Ohio use & addition to my Ruger #1 .405 Winchester.