There doesn't seem to be any walnuts here.
IMHO, American black walnuts are superior to Eurpean ones. Better tasting. The tree can be tapped for syrup. Despite the name walnuts are not nuts they're drupes (like peaches) Walnuts Trees are not neighborly as they produce a chemical to discourage other trees from growing.
Walnut Brook flows adjacent to Barton Hollow Road and a primitive trail provides access from Thatchers Hill Road (or so they would have you believe. Personally I think they lie). The homes on Turtle Court nearly bisect the preserve.
The background picture is that of butternuts. Even tastier. Aka white walnut