Different type of pond plants are treated differently. Hardy ones are generally left alone, tender ones are given winter protection. Van Ness Water Gardens should have some information for you. They offer an information sheet on wintering tropicals. One yard has a wild area at the back with weeds and a trash heap.
Weeds invade our yard from over there.
Another neighbor has ivy along the back of their yard, which comes through the fence and is impossible to keep out. A third neighbor has a couple of enormous fir trees that sap the water from whatever we plant along that part of the fence. He also has a shed with a bright blue tarp hanging on it that is quite visible from our yard. Dig a trench about 18 inches deep and stand-up the poly to slightly above ground level. The tree roots can be cut at the fence line, unless there is a chance of the tree falling.