It is unlawful for any owner to allow dogs, cats, cattle, horses, swine, sheep, chickens, or other similar animals or fowl to run at large within the corporate limits of the City. Any such animal or fowl at large may be impounded. Nothing in this section, however, shall be construed as prohibiting any owner of a dog or cat from walking the dog or cat with a leash, cord, chain, or other similar restraint not more than six feet in length or from transporting such dog or cat within a motor vehicle.