Base Layers
Pack with the coldest, wettest conditions in mind. Unless it's spring and you can really expect warm, sunny weather, you should pack enough warm clothes for the coldest temperatures that you're likely to expect at the given resort, even if the weather outlook is warm. Better to bring home a couple of clean shirts than to be shivering each and every lift ride. Pack according to the three-layer system, beginning with base layers. Bear in mind that base layers may get sweat-logged, smelly and uncomfortable, so pack a few shirts, and don't plan on wearing the same one each day. Microbial shirts are a good idea, because they'll fight body odor and add an extra day or two of wear time. Packing one shirt for every one or two days of your trip will help ensure that you have a clean, comfortable base layer every day. Base layers should be warm, breathable and moisture-wicking, so leave the white cotton T's at home, and opt for wool, polypropylene and polyester blend long-sleeve shirts. Don't forget some long johns as a base layer for your legs.
Insulation
Pack some warm jackets, sweatshirts, fleeces, vests and other insulation garments. Pack garments of different weights, for example, microfleece, heavy fleece, jacket, so that you can adjust insulation based on conditions. These won't be directly against your body, so you could get away with packing two or three separate garments for a weeklong trip if they're warm enough. Again, keep the coldest temperatures in mind when planning insulation. Don't forget some warm fleece pants.
Outerwear
Pack your snowboard jacket, pants and boots. In general, it's easiest to pack just one of each of these. Bringing extra jackets, pants or boots would be nice, but it would take up too much room to be worthwhile, especially with today's baggage fees on planes. Hanging these garments up overnight should allow them to dry amply for riding the next day.
Accessories
Don't forget essentials like beanies, snowboarding gloves and face,masks. Ideally you'll want to pack at least two pairs of gloves so that you can alternate and allow them more time to dry. Extra hats are also a good idea. Also remember goggles and sunglasses; a couple of pairs for different light conditions would be wise.
Casual Wear
Pack some nicer casual clothes if you plan to go out to a nice restaurant, bar or club. The type of clothes you pack will depend on the specific resort , so check the dress code at some of the establishments there, and pack accordingly. Don't forget casual shoes (or boots if you'll be doing any significant walking). Also bring a casual jacket and light gloves for walking around from place to place.
Swimsuit
Pack your swimsuit. When you're going to a place that averages 20 degrees, it can be easy to forget. However, if there's a hot tub, heated outdoor pool or indoor pool, you'll wish you had one. There are probably not many shops selling swimsuits in the middle of winter, so be sure to pack your own.
Extras
Pack standard items like underwear and socks; it's good to pack extra in case they get wet, sweaty and unusable. Pack both warm, heavier snowboarding socks and lighter casual socks. In fact, it's not a bad idea to pack two pairs of socks per day so that you have one to ride in and one to wear in the evening. Extra underwear is also valuable in case your snowboard pants soak through.
Final Tip
Given the amount of clothing and bulky gear that you need to pack for a snowboarding trip, you may find that you are running low on space. In this case, start to think multifunction, and consider how clothes can serve several purposes. While you don't want to wear your sweaty, nasty snowboarding clothes out to dinner or drinks, you could wear a casual jacket or sweater out one night and then use it as a insulating layer later on in the trip. Planning multifunctional garments can eliminate unnecessary clothing and cut out bulk.