Well hopefully I can add a bit here as I've spend a fortnight inthe arctic circle where it was -30C and have been camping a few times around -15C. Simply put trapped air is what will keep you warm, you want to have a thick a layer as possible between your skin and the "outside". Also moisture is not a good thing in extreme cold, try to avoid waterproof membranes as you get condensation that will freeze on the inside, try to go for natural and breathable fabrics where possible, you don't really need to worry about waterproof as the water outside will be ice and won't get into your clothes (except if kneeling or sitting in the snow where you can get melting), much more important is getting moisture from your body out.
Base layer - Merino wool 200 weight. I've played around with synthetic and silk base layers in the past, they're not bad but they're nowhere near as good as merino wool in terms of warmth, odour and comfort. Saying that though you could slip a silk base layer on underneath too for a bit extra. You'll be looking at £50-60 each for legs and top, e.g. Icebreaker.
Mid layer - Merino wool in the 400-600 weight range, probably better to go with 600 if you're going to be stationary. ~ £100 e.g. Woolpower.
Trousers - something with a good bit of synthetic insulation, manly because if you're likely to be kneeling or sitting you may get a little water ingress. Something like pile and Pertex or synthetic batting like Primaloft. ~£100 e.g. Rab photon pants.
Down jacket - I'd go with a jacket that has a more generous cut rather than the more athletic cut for active sports, also the more insulation the better. Definately keep away from the light weight down jackets (the ones with narrow baffles) as they won't give enough insulation. ~£200 e.g. Rab Summit or if you have the money you could go for a Canada Goose jacket.
Boots - you'll want something insulated and comfortable and most importantly not a tight fit as tight fitting boots will limit blood flow and lead to cold feet. There are lots of options here really, some options are Sorrel, Lundhags, Muck-boots or even ex-military arctic boots for a cheap option. Price anything from £50-£300+
Socks - again merino wool, they give the best warmth to weight ratio, you shouldn't need more than one pair on at a time if you get good winter/artic boots as above.
Hat - personal choice really, I'd probably go for something like a stretch fit beanie and a nice insulated hat on top so you can mix and match depending how warm you are. Also it depends if your jacket hood too, you may not need so much insulation if you have a good hood.
Gloves - again a layerying system will work best here, a thin liner glove so you can operate your camera while keeping some protection and dexterity and then an insulated mitten on top. Mittens are warmer than gloves because there is less surface area than gloves and your fingers are more mobile and can keep blood pumping, they also share heat kind of like jumping in a sleeping bag to share heat with someone with hypothermia.
That's about it really, It's not going to be cheap to be properly prepared but you really don't want to bugger about at -20C or colder with wind chill. You could try looking at the classifieds on outdoor forums or ebay to try and snag some bargains, or sell the kit when you get back. Make sure you go to a good outdoor store too, not many of the people working there would have much experience of extreme cold and would advise you based on what they have in the shop and assumptions, I wouldn't have known when I worked in one when I was in my early 20s at university.
