I have to say, I have mixed feelings about that. Using private property without permission to walk your dog is something I am careful not to do.
It is a particular peeve for me since I lost permission from one of the three neighbours who let me cross their property because some idiot was snowshoeing up to their barn and all around it. It wasn't me, but someone who followed my trails but went further and made their own. Of course this would be the middle of the three properties so now I am forced out once again onto the snowmobile trail.
A similar thing happened when I asked permission to ski a local golf course in winter, which would have been the fourth property owner in a row with the three above. Access was denied because the owner felt snowmobiles would follow my tracks and damage the greens. They would too, it's happened before.
In Canada we have private property and property owners have the right to say who uses their property. I've worked with our provincial, Ontario, Trespass to Property Act and it's very difficult for the property owners to exercise their rights when illegal use occurs. In one case near me a moron of a woman followed other illegal users in walking her dog and was scared almost to death when shots went off during hunting season. She made a fool of herself by complaining. She had no idea which municipality the property was in, or who owned it. She just went and possibly endangered her life and that of her kids and dog. She did not even know it was deer season and did not wear blaze orange. Kind of begs the jumping off a cliff question I think.
Sorry, I think preserving green space is admirable but I think you have no right to expect to keep using that property. Perhaps a fund raiser to buy it would be in order?