CT will never close Hammonasset State Park - that is by far the most financially lucrative park for the state. Hammo essentially pays for most of the rest of the state parks.
Another state park you might want to look into is Rocky Neck State Park, about 30 minutes farther north on I95.
Pachaug state forest is, if I remember correctly, all tent camping sites.
A couple CT state parks have "horse camping" sites! I did not know that until a few years ago. These are areas that you ride to (no room to trailer a horse in, not sure where you would start!), can set up a tent, and there are "hitching" posts and water troughs for horses.
