In order to create ponds for the cutting and harvesting of ice for the market, any persons or corporations may erect and maintain, on their own land, dams on streams not navigable or floatable, but emptying into tidewaters navigable in the winter, and may flow the lands above during November, December, January, February, March and April; but they shall draw off the water to its natural state by the 20th day of May yearly. If any lands are injured by such flowing, the owners thereof have the same remedies as in case of lands flowed by dams erected and maintained for mill purposes; but no right is granted by this section or section 656 to flow any milldam or any mill privilege improved or unimproved. This section shall not be construed as authorizing any persons or corporations to cut ice on any pond created as provided over any area the soil of which such persons or corporations do not own or lease or possess as tenants at will, or by reason of a valid agreement with the owner or lessee or tenant thereof when said owner or lessee is not the State and the pond is not a great pond.