Deer Archery season runs from Oct 1 to November 14 and again from Dec 1 to Jan 1. Deer Firearm runs from Nov 15 to Nov 30th. A person may hunt with a Bow during the Firearm season but must have a license that is valid for the firearm season (the archery hunter must wear orange during the firearm season as well).
Muzzleloading season in Zone 1 (U.P.) started Dec 7th and ended Dec 16th this year and the season in Zone 2 (Lower Peninsula)started Dec 14 and ended Dec 23.
There are a few special seasons (youth hunter Sept 22-23, late season antlerless on private land....)