According to The Little River Canyon National Preserve the Canyon Mouth Park is Closed, but the walking areas and trails, around the falls are open. But keep in mind, all bathroom facilities, on park grounds, are closed.
Here is a statement from the park:
“Following federal and state recommendations for precautions to help prevent the spread of the COVID-19 virus, Canyon Mouth Park is temporarily closed to visitors until further notice.
Visitors to Little River Canyon National Preserve are strongly encouraged to practice social distancing while visiting the Preserve.”