I hunted between Platte, SD and Winner, SD about 5-6 years ago and I'm going back again this year. I go with a group that has been making this trip annually for over 20 years, but this will be only my second time to go. This year, we're staying in Platte and hunting north of there near Kimball, SD.
We're hunting the last week of October, which is what we did last time I went. Of the three days we hunted last time, it was pretty cold one day due to a cold front, and was really nice and mild the other two days, like highs in the mid to upper 50's.
I have bird dogs and hunt quail a lot, especially when it's cold in January and February. All my hunting is done walking and no riding in a mule or on a 4 wheeler. I also hunt pheasants in the panhandle nearly every year, and hunted pheasants in the snow in Kansas last November. I've found in both quail and pheasant hunting, its real easy to overdress because of the walking involved. Dress in layers would be my advice. I've found that when you're standing around outside waiting to hunt, you should be a little bit cold/uncomfortable. Then when you start walking you end up about the right temperature. If the wind is really cold and howling, bundle up more, but have layers you can remove.
If you buy new boots, buy them now and start wearing them when walking, working in the yard, etc, and get them broken in. One year up in the Panhandle, my brother in law shredded his feet by wearing a new pair of boots that weren't broken in. The ground isn't real rough up there, but you'll want same tread on your boots for traction. I wear a pair of handmade pull on boots that James Leddy in Abilene made for me, others prefer lace ups. Just wear something that's comfortable and broken in. I prefer light to mid weight wool socks because they feel good on my feet when walking, and I've never gotten a blister while wearing them.
It has been my experience that the fields in South Dakota aren't nearly as big as those in Texas and Kansas. However, you'll still want to be in decent shape. You can't start hunting wild pheasants (meaning not on a "preserve") in South Dakota until 10:00 am each day, so the hours you'll be walking are greatly reduced as compared to Texas or Kansas. Also, the farmers we hunt on manage intensively for pheasants and leave blocks of uncut corn or milo in the fields, which is where the birds will be. My point being you don't walk the entire field like you might do elsewhere. Their CRP fields aren't as big up there either.
Get you a good pair of shooting gloves that you can hunt in. Big bulky gloves might be warm, but they won't allow you to shoot. If you don't wear gloves and your hands get cold, you'll be miserable.
Sorry for the length of this!
Have fun in South Dakota! You'll see more pheasants by lunch up there than you will in a full weekend of hunting in other places. It's definitely worth a trip up there.