I've been contemplating the same thing. Never been hunting.
From what I understand, your state DNR sets the rules for taking wild game. One of those rules is the minimum caliber required to humanely harvest wild game. Some states it's legal to take a deer with a .223, some states not.
luckily ohio DNR hunting regs state "Unless otherwise indicated, game may be taken with longbow, crossbow, or any caliber handgun, rifle, shotgun (10 gauge or smaller), or airgun. Be safe and choose the appropriate method for the species."
but also states for deer
Shotgun – 10 gauge or smaller using one ball or one rifled slug per barrel (rifled shotgun barrels are permitted when using shotgun slug ammunition) – the shotgun cannot be capable of holding more than 3 shells, unless it is plugged with a one-piece filler which limits the capacity of the gun to 3 shells. The filler must be such that it cannot be removed without disassembling the gun.
Muzzleloading rifle - .38 caliber or larger
Handgun – 5-in. min. length barrel, using straight-walled cartridges .357 caliber or larger
Longbow – min. draw weight 40 lbs., includes compound and recurve bows. The arrow tip shall have a minimum of two cutting edges which may be exposed or unexposed minimum 3/4 inch width. Expandable and mechanical broadheads are legal. Poisoned or explosive arrows are illegal.
Crossbow – draw weight no less than 75 lbs. The arrow tip shall have a minimum of two cutting edges which may be exposed or unexposed minimum 3/4 inch width. Expandable and mechanical broadheads are legal. Poisoned or explosive arrows are illegal.
so bite me ODNR... still allowed to shoot coyote wild boar Groundhog, Fox, Raccoon, Skunk, Opossum, Weasel, Squirrel,Cottontail Rabbit, Ring-necked Pheasant, RuffedGrouse, Bobwhite Quail, and Crow