You may carry in all parks... Michigan has complete preemption of local ordinances that deal with firearms.
You may want to carry this handy chart: http://www.miopencarry.org/moc_files/brochure.pdf
Post on here when and where you are when in Michigan; we have meet-ups quite often. Enjoy your trip!!
There is some argument here whether Michigan will honor a Non-resident license... I believe they will for OC (they definately won't for CC). The state police MAY see it otherwise. I'm sure some will chime in here soon.