The public waterfall is never closed although during lockdown I can imagine local city officials might have closed off the site to prevent crowds from forming since it is a popular place. I imagine for anyone interested in visiting, at the moment they want to go, they will have to see what the current conditions are as far as restrictions to travel and to public gatherings are. Back in June, most of the restrictions were already lifted and most places were open. The waterfall hot springs themselves have no "entity" guarding them so I cannot imagine they were a site that could be open or closed easily, other than by the local city government in Saturnia placing road blocks to prevent people from entering.
Considering the year we are having, there are no easy answers to the usual questions. We'll see how things develop in 2021! ;-)