I think the code reads to 1)"Regulate",- they can regulate animals. 2)Restrain- they put on a nose ring, halter, or lease; they can put in a cage or pen, they can put in a fenced in area. 3) Prohibit the running at large- means they can say you must keep your animals on your property, and if they feel that the animals can hurt themselves running "at large" on your property they can demand you to do your own "restraining" of their choosing.

Later in the ordinance they claim to be able to confiscate and sell your animals if you owe them $ from breaking ordinances, plus court costs..

He's not citing an ordinance, he's citing Ohio State Law that defines the parameters of city ordinances:

http://www.animallaw.info/statutes/stusohst715_23.htm

Title VII. Municipal Corporations. Chapter 715. General Powers. Streets and Parks. 715.23 Impounding animals

It simply gives cities pretty much unlimited power to regulate all livestock within their city limits, with an exception for dogs, which are treated differently in 955.