You going sometime soon? Around December the temps tend to plunge and Jan-Feb can be really cold, somewhere around -40C, potentially with some wind and blowing snow making it feel even colder. Highly recommend good outside set, with winter boots, gloves and the rest of clothing meant for that sort of weather, especially if you expect you would need to be outside for a while. I like the overall type pants and winter rubber boots big enough to fit wool socks in myself. :P Might be difficult to buy good quality stuff if you live somewhere much warmer. Probably worth asking whoever is hosting you for some help there. They might even have extra sets available already. Houses up there are typically very warm, so nothing special needed for inside use. Otherwise maybe a camera that is good in low light if you like to take pictures. Should get some good northern lights and stuff if you’re up there a whole month.