I hunt pheasants in Montana every fall for ~6 weeks, usually starting around 20 October. Season usually opens the first weekend of Oct. By the twentieth most of the early season crazies are gone. Also, it's usually (not always!) cold enough to keep the rattlers asleep. I often stay through the first week or two of December. Once the snow flies wild roosters get very jumpy, no doubt because they're easier for raptors to see. Also, the weather can be brutal. Look at my avatar photo. That was first week of December and just below zero F. I had just shot my one and only lifetime triple. Had given up because too cold and birds too spooky. While walking back to the truck my Lab went on point ten yards away. She held them long enough for me to get my hands out of my pants pockets and A5 unslung. Fortunately, all five were roosters and cackling. Didn't have to worry about shooting a hen. And I also had an empty bag so I could shoot three. Bagging a triple of wild pheasants is a rare thing indeed. Farm raised birds often need to be kicked in the air so a triple on them is not as rare.
The next year a storm blew in the weekend before Thanksgiving that left drifts more than twenty feet deep. And I've seen that happen more than once. Even though you plan to hunt south of my stomping grounds (I'm typically less than 100 miles from Canadian border), I would still advise going the week before Thanksgiving if you can swing it. Ideally you want to be there after the opening week lunacy, late enough so you don't get caught in a rainstorm (the mud on the prairies can be brutal), and before the deep freeze sets in. Snakes can be a concern if you have dogs that aren't conditioned for them. A good outfitter should have dogs that are educated. After October even if you see one, it likely will be sluggish and not aggressive. Personally I'm not concerned but I did have a dog get bit once in November. Very freaky. Luckily prairie rattlers are not the most venomous and Pearl recovered ... in time to tear herself up on a fence getting our last bird for the season. Twenty stitches on Thanksgiving weekend.