The December archery season is when I was thinking about doing this, still hunting for deer with the recurve and carrying my 410 pistol for the (possible) third shot on a squirrel.
It's going to come down to hunting one season or the other. If you are carrying a bow and arrows with broadheads suitable for deer you will be considered hunting deer. If you are possessing a handgun with shotgun shells, you will be considered hunting small game. You can not mix both. You could hunt small game with the bow and any broad head without the handgun or with the handgun and small game points.
In other words, if you are doing the archery deer hunt, you can not possess and use a handgun.
Page 22 of the Michigan Hunting Digest 2019.
Archery Deer Seasons
During the archery deer seasons, it is unlawful to possess or carry afield a pistol, revolver, or other firearm while bow hunting for deer.
Exception: This prohibition does not apply to the following:
• An individual who is properly licensed to hunt deer with a firearm and is in an area open to firearm deer hunting during the early and late antlerless season, liberty hunt, independence hunt, and the Nov. 15-30 firearm deer hunt.
• An individual who is properly licensed to hunt deer with a firearm and is an area open to the muzzleloading deer season in zone 2 or zone 3.
• Pistols carried under authority of a concealed pistol license or properly carried under authority of a specific exception from the requirement of a concealed pistol license. However, a concealed pistol license does not authorize the individual to use the pistol to take game except as provided by law.
