Hi Dave,
Currently here in MS we can bowhunt straight through from the opening of archery season until the end of January. The license is cheap for residents.
Traditionally our archery season opens on Oct. 1, and gun season with dogs opens the third Saturday in November. Primitive weapons season (no dogs) opens Dec. 2 and closes Dec. 15. Then it's guns without dogs from the 16th until the 23rd, and then guns with dogs again from Dec. 24 until Jan. 20. Primitive weapons season then runs to the end of Jan. There are some variations to this schedule in the extreme southern part of the state, with 15 days taken off the front end of the archery season and added back to the last primitive weapons season, making the closing Feb. 15. Does are legal on private land, but only part of the time on public land. It's difficult to keep up with.
Next year everything may change completely. There is a rumor that the season may run from Oct. 1 until the end of January, all legal deer hunting weapons legal all the time! This will be a significant blow to archery and primitive weapons hunters, and may do real damage to the sporting goods stores who have archery and primitive weapons inventories to sell. We bowhunters will no longer be able to hunt deer that haven't been harassed by the gun hunters yet, if this takes place.
I love hunting in your state, even though I have to pay $175 for each season I hunt in. Missouri is very progressive, apparently with wildlife professionals managing the seasons. Down here it's the politicians.