If you plan a trip, take it, don't let the weather dictate what you are going to do. No matter what the temp is, you can dress and prepare for it, and hunt accordingly. I just got back from 3 days of hunting in 0-10 degree weather in SD with wind chills in the negatives on 2 of the days.
From an avid late season pheasant hunter and ice fisherman, here is what I have found to help out.
1. Base Layer. Very valuable layer here, I generally use a cotton thermal layer, like some long johns and a similar shirt. Sometimes I will go with a Nike or Under Armour dry-fit type that wicks the sweat away.
2. Socks. I usually wear just a thicker cotton sock. I have found that a big key with my feet, is that I can't dress warm enough that they start to sweat. Sweat=moisture=eventually you'll be wet and cold. Sometimes I will go with a dry fit sock then a wool sock over.
3. Middle Layer. Generally a hooded sweatshirt. Sweatpants if I'm going to be wearing some bibs/overalls/snowpants.
4. Outer Layer. Carhart jacket on the upper body. Usually just my normal pair of pheasant hunting pants on the lower body. If enough snow or cold enough, I'll sometimes where some bibs instead.
5. Head. You Lose the most of your heat through your head. I wear an Under Armour facemask, similar to what football players would wear under their helmet. Allows me to cover my face if I need to, and keep my face open if I need to. Stocking cap over that. I have worn ski goggles before while pheasant hunting. 2 or 3 years ago I hunted the final day of the MN season in (from what I remember) about -20 air temp and -40 wind chill, I had to keep every part of my body covered, so the ski goggles helped there.
6. Hands. I struggle keeping my hands warm, even in 50 degree weather. I still haven't found a perfect late season hunting glove. I have very thick warm snowmobiling gloves, but I can't always get the safety on my gun clicked off when a rooster goes up as quickly as I'd like while wearing those. I generally wear one thicker glove on my left hand, and one slightly thinner glove on my right hand. Then I also put a handwarmer packet in each glove. I have not done this yet, but a friend recently told me to put a latex rubber glove on first under your gloves.
To sum it up, you will be surprised how quickly you can warm up in the field while walking. On these 0 degree days we have right now, dress light enough that you won't be drenched in sweat, but heavy enough that you aren't freezing for the first hour until body heats up. Remember its easier to take layers off than add layers on. Once I am moving in a field, I prefer to just keep going the rest of the day. Taking breaks allows your sweat to dry and freeze on you, then you just have to warm up again. Once your warm, your warm though.
Other things to consider when hunting these 0 degree temps.
1. Water: Still important for you and the dog. How will you keep it from freezing? Generally just keeping it in the cab vs. the bed of the truck is enough.
2. Small shovel in case you get stuck in an access if there is lots of snow.
3. Extra set of clothes in case something goes terribly wrong (you break through cattails and are now drenched).
4. Let a friend know where you are hunting at. Again, if something goes terribly wrong (you step in a hole and break your leg) you could die overnight in these temps. Always carry your phone on you while hunting, but some parts of SD also have pretty poor reception.
