Wearing layers of thermal clothing is a good idea, especially light weight/warm/quick dry gear that packs small and can be put on/off easily if the weather changes during the day (not cotton, but wool, polypro & fleece).
Basically, you will need:
- winter down sleeping bag (-11 degrees Comfort Rating minimum),
- winter 4 season tent
- winter sleep mat
- thermal sleeping bag liner
- a waterproof jacket with a hood and over pants,
- waterproof & insulated gloves or mitts (2 pairs),
- lightweight wool or thermal gloves liners (2 pairs),
- medium 200+ weight fleece,
- ski pants (water resistant and thermal/insulated) & or extra heavy thermal pants (not cotton or jeans),
- watertight water bottle – 1 litre capacity that can hold boiling water,
- overnight pack 75 to 85 litre top loader
- knife, fork, spoon, plate and mug (durable and lightweight),
- hand warmers & feet warmers are great if you feel the cold easily
Each of these items can be rented. Just don't forget to write your guide beforehand!