Concentrate on your head, feet and hands.
Head will dissipate most heat as the blood circulation won't be restricted, so it's important to use good gear and thus preserve body heat. I use a custom made balaclava when it's really cold and/or windy. Using several layers is wise since you can adapt to different temperatures by adding, not changing gear.
Feet will get cold if you lose body heat and your natural mechanism starts to restrict blood circulation. It's important to have enough room, just stuffing extra socks in boots is not going to make it. If you don't require mobility some form of Ansitzsack to cover your feet and lower body would be easy (you can use sleeping back if it's not noisy). Obviously works best in enclosed high seat. I've been very pleased with these (just the first UK link I found)
Sorel Glacier Snow Boot - Protection down to Minus 70 degrees Centigrade | Countryside
Hands are even tougher than feet. They suffer from same restricted circulation, but usually you must use them thus discard at least the outer layer of protection. I use some form of thin gloves, usually cheap goat skin mechanics gloves, which stay on at all times. On top of them I have warm mittens (don't use gloves, you want to keep fingers together for warmth), or I can tuck the hands inside my BIBs if I need to warm them up a bit.
For the rest of the body I just use an insulated BIB, of course some form of inner layers, and maybe fleece blankets to cover my thighs and shoulders. If mobility is required, you can use large size fleece jacket/shirt on top, it really cuts down on noise. I've used these also in open high seats while snowing, it just means you have to dry them up properly before next use.
Oh, and don't forget separate gear for carcass retrieval etc. especially if you need to continue the high seat work. I usually try to shed a layer or two, change mittens to leather working gloves and maybe use a boonie hat (stops snow drift from low branches down your collar) when it's time to retrieve the beasts.