What are the effects of wild and scenic river designation on private landowners within the river corridor?

Under the Wild & Scenic Rivers Act, designation neither gives nor implies government control of private lands within the river corridor. Although many rivers include private lands within the boundaries of the designated river area, management restrictions would apply only to federal lands. The federal government has no power to regulate or zone private lands under the Wild & Scenic Rivers Act; however, administering agencies may highlight the need for amendment to local zoning (where state and local zoning occurs). People living within a river corridor may use their property as they had before designation.

Source
Interagency Wild & Scenic Rivers Council