I have been unable to find a mowing ordinance case that was heard in a superior court that has jurisdiction over Potsdam, New York.
However, there are interesting court cases in other jurisdictions.
BELL v TORONTO (1996, Ontario)
Sandy Bell cultivated a natural garden in the front yard of her Toronto home. She was convicted in a lower court for violation of a city by-law that prohibited excessive growth of weeds and grass. The appeals court ruled in Bell's favor, finding the law void for vagueness and in violation of the free expression clause of the Canadian Charter of Rights and Freedoms.
BERGER v MAYFIELD HEIGHTS (1998, Ohio)
To deal with complaints about a particular vacant lot that was left in its natural state, Mayfield Heights ammended their weed control law to force all vacant lots smaller than a stated size to be cut of all vegetation (including trees, according to the Court's reading) in excess of eight inches. Berger won.
Bauer v Village of DeForest (1999, Wisconsin)
Bauer was told to remove noxious weeds from her property. She sued, lost, appealed, and lost again.