Most people start Memorial weekend, but with the current reservation system (out of Indiana), reservations for "state parks" would have had to have been made last November.
My humble opinion... This reservation "system" is akin to calling a radio station when you hear the special sound to try to win the jackpot prize. On the specified day (6 months prior to camping) we have two phones going and at least one computer trying to beat 100's of other people who are trying to get the same lot!
When we were kids we would get whatever lot we could (reservations weren't allowed), then at 4 Am the next morning my dad would sit on the ranger's door step to be the first one in line to change to the lot we wanted.
Anyway, most state parks in Michigan open late March to April. Some, like Ludington, are open almost if not all year-round. My brother and his family like going there in the winter. It is a totally dofferent place that time of year...but thhe bathrooms are closed!