Matt,
The bow season runs till January 10th, typically the rut slows and the gun season starts. Most of the hunting during shotgun season is "drive" hunting much like bird hunting. I don't know about killing every deer in the woods but typically the majority of the deer harvest is during the shotgun season.
The bigger bucks seem to find away around drive hunting and make it through the shotgun season and a week or two after it is over with some cold weather they will try to save all the calories they can by eating in the daylight hours again. This can be a great time to shoot a nice one. This also runs along with late muzzleloader season during which time driving deer is not as common of practice. Hope this answered your questions. Welcome to Iowa!