The park is open all year. Check online for available sites, but it's very likely that some would be open. Not sure we've ever seen turkeys there.
Several sites are available for that time of year. I have seen turkey on the north end of the park and a hen an chicks on May 26th by the swinging bridge .
I'm sure there are campsites. But I don't know about Hunting on the park grounds. Try Michigan DNR for that one.
I have actually heard Turkeys during my hikes. They do have spring sites open. Good luck!
Now that you mention it, I've never seen any turkeys there either.
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