Ohio has open carry by default, there is no law against it so it is legal. I don't know of many people that do open carry.
Theoretically, Missouri is the same. However, our preemption law does not cover open carry, and some cities have outlawed the practice.
Dunno about Missouri, but the Ohio state constitution guarantees the right to keep and bear arms, but state law used to prohibit concealed carry. The cops naturally assumed that meant all carry was illegal and arrested anyone they saw with a gun. Several years ago, one of the victims of this over-zealous enforcemt decided not to roll over, and took it to court. My recollection is that he lost in the lower courts, but he appealed to the state supreme court and they decided he was right.
Basically, the ruling said the state can regulate the mode of carry, but cannot prohibit something that is expressly guaranteed in the constitution. Therefore (said the court), since the state legislature had prohibited concealed carry, that meant open carry was legal.