§ 301. Lands lying open. When the owners of adjoining lands shall choose to let them lie open, as provided in section three hundred, neither of such owners shall be liable to the other in any action or proceeding for any damages done by animals lawfully upon the other's premises going upon the lands so lying open or upon any other lands of the owner thereof through such lands so lying open. Either owner of any lands so lying open and adjoining may, unless the agreement is for a specified period, and after such agreement has expired may then have the same inclosed, by giving written notice to that effect to the owners or occupants of the adjoining lands, whereupon it shall be the duty of both parties to build and maintain their several proportions of a division fence.