You probably don’t want more than three layers on at a time. But you do need to pack multiples of each, especially those body-hugging baselayers that inevitably get sweaty. Make sure they are constructed from performance fabrics that wick moisture away from your skin. Warmer, insulating mid-layers (like a long-sleeved fleece) are a must for the slopes and lighter layers (think vest) are nice when you’re walking in and out of heated shops on Main Street. A waterproof ski coat and pants/bibs are also a necessity. Outer layers should have a minimum waterproof rating of 10,000 mm.
Pro tip: Never put your coat in checked luggage. Wear it or carry it on. If your luggage gets lost, you’re still warm while waiting around filling out forms and you don’t have to buy an overpriced shell in the airport. Additionally, you might want to wear a pair of lightweight liners underneath your gloves or mittens on really cold days, a beanie or ski mask under your helmet, and a neck gaiter in conjunction with your mid-layer.