Stating where you can hunt, or shoot, do not violate our rights as gunowners.
Much.
Rules concerning private property don't either, except in some people's minds, they do.
Rules covering what you can own, posess and carry, do, IMHO.
However, no right is absolute. This is a fundamental concept in our society. Your right to swing your fist ends at my nose, etc.
Its complicated situation. Near me is a park (its desert, but they call it a park) a mile from our range. The park is posted "No Firearms". I feel that is wrong. They would be entirely correct to post it "No discharge of firearms allowed", but not "No Firearms", again, in my opinion.
For some reason, our public officials just cannot make the distinction between the mere posession of arms (for personal protection, mainly), and the use (discharge) of arms for recreation. SO, they put up signs saying NO FIREARMS, when what they ought to do is post NO Shooting.
Also, one often hears of a situation where someone defends themselves, and while exonerated of the shooting, gets charged with "discharging a firearm within...." There ought to be an exemption for that, but often isn't.
Call/contact the city attorney and ask what ordinance/regulation/law gives them the authority to post it the way they have. I know of one case, where after a few years of arguing, one city park which was posted NO Firearms was finally forced to change the sign, as legal CCW was allowed under state law, and the state does have a no local preemption law. It took a while, but in the end, it was done.
Also, it was mentioned something about a highway. There are usually regulations about being able to shoot within a certain number of feet from a public road. Perhaps someone measured the distance and determined the park was too close to the highway. A situation that could have existed, and been ignored for decades. IF thats the case, then they are technically correct to ban hunting in that area, even though they never did before.
Liability, you know.