Things that’s catch you out, from recent experience and echoing some of the above.
As all the photographic setting’s side has been pretty much covered… This is primarily assuming your going to be shooting somewhere quite cold and a remote dark location.
Take a second camera! Beg, Borrow, Hire a second camera, if anything like me you travel thousands of miles to Norway specifically to photograph the Aurora and your camera dies you’ll be devastated! Don’t think “It’ll never happen to me” I had two cameras with me on the shoot. A great show of the lights in Alta, Norway about 3/4 of the way through the shoot the D700 (which has a very low shutter count) died with “Error” possibly due to cold. Thank goodness I’d packed the D300 too!
Take a lot of batteries they die considerably quicker in the cold. Keep them in a pocket next to your skin, so your body warmth keeps their temperature up. Buy more than you have already, you will kick yourself if your batteries die before the Aurora does.
Working at night! Take a headlamp and modify if required with a red lens (this can be done with repair tape for car tail lamps) Make sure its simple to operate (Big On / Off buttons etc.). Why red light? Well red light helps your eyes recover quicker than from a show of white light. Also take a torch (with coloured lenses if you have them) and lots of spare batteries for torch and headlamp. Remember to turn the lamp off when you’re shooting. You can also use a torch for light painting the foreground if required. Take a couple of chemical glow/light sticks in case of emergency, if your torches are flat by the time you come to pack up and walk back, you’ll be stuck without a light source.
Take a 3ft or so, square of brightly coloured Rip Stop nylon (or similar), when you get to your location put it on the ground (Snow) to put your camera bag & kit on. This keeps your bag drier and gives you somewhere to place items when you take them out of your bag less chance of loosing something.
Working with your kit on, go out at night and practice photography at night up front, especially if you have never shot at night before. At night everything is different, Looks different and operating a camera wearing 6 or 7 layers is very different. Know your camera inside out and where all the controls are… Set up the camera to the basic night photography (Aurora) settings before you set out.
As per other answers, get really good boots and thermal socks, and don’t just believe some salesman that says their good! Remember you are likely to be stood in the snow probably for hours. If your anything like me you wont want to leave your cameras and go and warm up somewhere, so your effectively rooted to the spot. Test your boots and socks BEFORE your trip. The cold will kill your trip stone dead if your freezing and cant stand the cold any more, and that would be a disaster if the Aurora was still in full flow. Many Togs around me packed up because they couldn’t hack the freezing -21 temperature.
Get some GOOD gloves, flip top mitts that leave the top of your fingers free to operate the camera, I used Lowe Alpine Turbine Convertible Mitt with pure silk ultra thin liners underneath, with the option of snow mitts to cover the lot if it got serious cold.
Take some hand warmers not only can you use these to keep your hands warm, they can also be used to stick in your socks, or keep your batteries warm, and stop your camera freezing up.
Get a spare fleece snood! Once your camera is set up you can put the snood over the camera and still be able to access the controls. This will help to stop it freezing and if you slip a hand warmer inside this will help too.
Don’t forget to take some food and drink! Chocolate, energy foods, and if you have the option hot soup and or drink in a thermos flask or take a camp stove.
Check your tripod. If its not got an insulated leg or legs then wrap at least one of the legs with foam particularly if its Aluminium. Use pipe insulation wrapped over with something like a tennis racket handle grip tape or similar. On my second camera the Ali tripod leg froze to my hand when packing up! You might want to make sure you have spikes on your tripod feet for better stabilisation in the Snow.
Take your UV or lens protection filter off for the duration of the shoot, this stops condensation getting trapped between the front element of the lens and the filter. Don’t try and take this off halfway through the shoot it will be difficult and might have frozen to the lens threads. Use your Lens hood for additional protection and help stop the front element frosting.
Be careful with remote releases (Also remember spare batteries for this). Remember in extreme temperatures the cables can become brittle and break at the plug. If your planning a extremely cold trip perhaps insulate the cables. In fact anything plastic could be subject to becoming brittle that includes Camera socket covers, plastic parts on a tripod etc.
Regarding your proposed location… If its possible to recce your shooting location in daylight its a real help, things look very different at night and if you are out in a remote dark location setting up some landmarks or placing some markers can really help you when you return in the dark. This also gives you the opportunity to get an idea of composition for the shoot. Its also sensible from a safety point of view, a recce could prevent you setting up on a crust of thin ice over 2ft of snow. You usually only find this out when you stab the feet of the tripod into the ground and you drop 2ft into the snow!
After your shoot, introduce your camera back into warmer temperatures gradually, don’t just wack it straight into a hot room. Leave it in a cool lobby in the camera bag so that it gradually reaches room temperature, perhaps moving the bag gradually into a warmer place. If the camera was subject to frosting up (Mine were white!!) I wipe them down with a microfiber cloth then I put them in a sealed bag containing a large bag of silica gel to take some of the moisture away.
Hope you find this useful