The county legislative authority of any county of this state shall have the power to designate by an order made and published, as provided in RCW
16.24.030, certain territory as stock restricted area within such county in which it shall be unlawful to permit livestock of any kind to run at large. No territory so designated shall be less than two square miles in area. RCW
16.24.010 through
16.24.065 shall not affect counties having adopted township organization. All territory not so designated shall be range area, in which it shall be lawful to permit cattle, horses, mules, or donkeys to run at large: PROVIDED, That the county legislative authority may designate areas where it shall be unlawful to permit any livestock other than cattle to run at large.