Laura Hendricks, the Kalkaska County Planning, Zoning & Soil Erosion administrator indicated that you may cut down any tree on your property up to 500 feet from the lake, even on the shoreline, without applying for a soil erosion permit providing you do not remove the stump and roots.
The State of Michigan’s Department of Environment, Great Lakes and Energy (EGLE) in an overview of Part 91* indicates that:
“A permit is generally required for any earth change activity which disturbs one or more acres of land or which is within 500 feet of a lake or stream.”
So any vegetation that changes the earth generally requires a permit. Bottom line: when in doubt, apply for a permit.
You can find more information of Part 91 at:
https://www.michigan.gov/egle/about/organization/water-resources/soil-erosion.
*Soil Erosion and Sedimentation Control of the Natural Resources and Environmental Protection Act.