A low-speed vehicle may be operated on any highway on which the speed limit is not more than thirty-five miles per hour. A low-speed vehicle may cross a highway on which the speed limit is more than thirty-five miles per hour. Nothing in this section shall prevent a county, city, or village from adopting more stringent ordinances governing low-speed vehicle operation if the governing body of the county, city, or village determines that such ordinances are necessary in the interest of public safety. Any person operating a low-speed vehicle as authorized under this section shall have a valid Class O operator's license and shall have liability insurance coverage for the low-speed vehicle. The Department of Transportation may prohibit the operation of low-speed vehicles on any highway under its jurisdiction if it determines that the prohibition is necessary in the interest of public safety.