Michigan has over 3000 miles of Rails-to-Trails MUPs. There are many trails that can be can be linked together to go where you want to go. My wife and I rode a 1000 mile loop around the state, rode from Ludington to Grosse Ile (across the state), and from New Boston to Alganac. The last two rides were parts of longer tours.
We rode parts of the South Haven to Port Huron Route west to east. We turned south at Jackson and headed south east toward Lake Erie. We used the MUPs, when we came across one that was heading in the direction we wanted to go. There are a lot of quiet back roads in Michigan.
Horses are not an issue, and motorized vehicles were prohibited on the trails we rode on. I suspect some sections may be used by snowmobiles in the winter.
Do a search; there a number of map sources available, e.g. –
https://www.traillink.com/trailsearch/?state=mi