A person who owns or possesses livestock may not permit the livestock to graze, remain upon, or occupy a part of the right-of-way of:
(1) a state highway running through cultivated areas or a part of the fenced right-of-way of a state highway if in either case the highway has been designated by agreement between the transportation commission and the secretary of transportation as a part of the national system of interstate and defense highways; or
(2) a state highway designated by agreement between the transportation commission and the secretary of transportation as a part of the federal-aid primary system, except as provided in 60-7-202.