Can the federal government regulate or zone private lands under the Wild & Scenic Rivers Act?

No. Under the Wild & Scenic Rivers Act, the federal government has no authority to regulate or zone private lands. Land use controls on private lands are solely a matter of state and local zoning. Although the Wild & Scenic Rivers Act includes provisions encouraging the protection of river values through state and local governmental land use planning, there are no binding provisions on local governments. In the absence of state or local river protection provisions, the federal government may seek to protect values by providing technical assistance, entering into agreements with landowners and/or through purchase of easements, exchanges, or acquisition of private lands.

Source
Interagency Wild & Scenic Rivers Council