When it absorbs your perspiration, it will stay wet. You can wash out long underwear at night, and it'll usually be dry by morning, thanks to those modern fabrics. A light shirt or turtleneck to wear over the underwear. A sweater of wool or fleece for insulation and warmth. One lightweight and one heavy parka to allow for changing weather.
Outer layers are bulky and take up lots of luggage space.
You don't need several outfits for a multi-day trip unless you perspire heavily. You can adjust for temperature changes by what you wear underneath. A helmet not only will protect your head if you bang it on hard-packed snow, but it will keep your body nice and toasty. You may find that with a helmet, you won't need the middle fleece layer. Bring several pair, and be sure they aren't cotton.