As I understood the debates, the legislature felt that if the local governments could only close an entire park that they would be more likely to leave most parks open. That crystal ball really forecast wrong perhaps on the assumption that the local governments would act reasonably and take the state's lead in opening all parks and only closing those where there was some compelling interest - perhaps such as a park that was nothing but ball fields.
Now, I don't see that the state statute prohibits the closure to dates, time frames, etc.
As it stands, I ultimately think the only solution will be to take away local option on parks.