According to the National Park Service's Civil War Soldiers and Sailors System there were almost 40 different individuals with the name Charles Moore who served in Ohio volunteer units during the Civil War. Your individual would have been rather old to be a soldier in 1862, having his 53rd birthday in the year he died. My guess would be that if he was a soldier it was probably not in a cavalry unit, perhaps not even an infantry one, because of the physical demands. Obviously this person, if he was a soldier, would not had belonged to any of the the higher numbered infantry units organized after December 1862, which would be those numbered above 127th (127th Ohio, organized in September 1862, was a "Colored" Regiment that got redisignated in the U.S. Colored Troops) and the new organizations
for the 18th and 60th Ohio Regiments that formed late in the war. Of the two Heavy Artillery Regiments, only the First Ohio Heavy Artillery existed before December 1862, so that elimates the first two soldiers on the sustems list because they are the same soldier.
After narrowing down the soldiers listed on the CWSSS you could look up info on those left by checking where they are listed in the official Ohio Roster that can be found in many larger library reference collections in your state. It would be kind of time consuming. The list could be further narrowed down by dismissing soldiers whose units had no companies from this man's home county. The Ohio in the Civil War site provides info on what counties the different companies of each regiment came from.
What clue, other than the date of the man's death, do you have tha he was in the Civil War? Is there a GAR marker next
to his grave?