For every trailer, semitrailer, or pole trailer, not exempted by § 56-3-120(5), the biennial registration fee is twenty dollars. The Department of Motor Vehicles must include in this classification every trailer, semitrailer, or pole trailer designed for carrying property, except house trailers, utility trailers, those trailers and semitrailers exempted by § 56-3-120(5), and boat trailers as otherwise provided in this article. Semitrailers or pole trailers weighing less than five hundred pounds with load capacity of less than one thousand pounds and trailers and semitrailers with an actual unloaded weight of fifteen hundred pounds or less and carrying a load capacity not exceeding twenty-five hundred pounds and which are designed, adapted, and used exclusively for agriculture, horticulture, or livestock-raising operations or for lifting or carrying an implement of husbandry need not be registered or licensed.