to the OP....what is the nature of this public hunting land...ie is it trully public...ie owned and controlled by some goverment entity (city, county, state, federal)? if it is prettly local city/county there is more a case for usage focused on the local community vs a wider state/federal communicty.
Why is it considered "hunting" land....is it a formal designation or just what people have used it for for a while?

If it is truly public...there is not much basis other than common sense to prevent people for using the land during hunting season

As noted in lots of posts there is a huge potential for conflict between different sporting uses. A trail close to me in a county park that is popular with hikers and equestrians has managed to keep mtn bikes of the trails for over 20 years.....partiall because of some irresponsible behavior 20 years ago.

I am pretty sure land use laws vary widely and some types of public lands are off limits to hunting.

Where I grew up (north central Montana) most hunting is done with permission of the landowner only...and that includes BLM lands the landowner has leased. Much of this is to prevent damage done by hunters, both clueless (open a gate and leave it open), drop a cigarette or malicious like shooting machinery, out buildings and cattle.