What Michigan camping areas let you cut down trees and build campsites?

All National Forests allow you to harvest the firewood that you will consume for overnight camping and allow dispersed camping in most areas as long as you camp a hundred feet off trail, road, or wetland. Also, research the designated Wilderness Areas in Michigan. [Yahoo Answers does not allow me to include all of my sources, so you will need to search.] National Forest: Hiawatha National Forest Huron-Manistee National Forest Ottawa National Forest Wilderness: Beaver Basin Wilderness Big Island Lake Wilderness Delirium Wilderness Horseshoe Bay Wilderness Huron Islands Wilderness Isle Royale Wilderness Mackinac Wilderness McCormick Wilderness Michigan Islands Wilderness Nordhouse Dunes Wilderness Rock River Canyon Wilderness Round Island Wilderness Seney Wilderness Sturgeon River Gorge Wilderness Sylvania Wilderness

You've gotten excellent advice from the first couple of answers. I would add that you need to check with your regional forest service or DNR about whether it is even permissible to collect deadfall. Many of the nation's forests are suffering from devastating infestations of destructive insects and diseases, especially from invasive beetle species. There have been restrictions in my homestate of Pennsylvania in recent years banning even disturbing or moving dead wood because it helps the spread of the beetles. Yes, everyone fantasizes about "primitive" camping, but if everyone did so the forests would rapidly become scarred and damaged. I "rough it" all the time in backcountry camping where we hike in several days, but we bring modern gas-fired stoves for cooking, battery headlamps for light and lightweight tents for shelter. The experience is just as gratifying and we leave the woods looking just as we found them.