The key to beating the winter weather of this region is to look for cold-weather gear that includes an outer layer that is made of gore-tex. There are countless makers (and expensive ones at that) of ski parkas and snowboarding pants that have a very chilly cold rating (to temperatures of -20ºF and lower), but are only water resistant, not waterproof. This is because in most cold-weather regions, cold weather means snow. North Cascades weather does not do us the favor of being so predictable; rain can fall in January just as in July. In North Cascades National Park, it is essential that your cold-weather gear also be waterproof.
Choose clothing that is waterproof and breathable. In my experience, gore-tex is the best bet. Gore-tex is 100% waterproof as well as being very breathable; gone are the days of youth--with the fluorescent yellow 'slicker' that prompted every inch of covered skin to sweat so that the inside got as slick as the outside. Such old-school gear was fine while we waited for the school bus, but at North Cascades NP, as always in this kind of rugged terrain, only the best will do. When in the backcountry for days at a time in winter, it's not comfort we're concerned with, but safety.
The proper way to layer in extreme weather such as winter in North Cascades NP is with synthetic fabrics close to your skin (no cotton!!!) with a few layers of wool over the undergarments and then outerwear that is built both for extremely cold, as well as for extremely wet, weather. A few thinner layers of wool work better than one thick layer because you can use this to change the amount of warmth you need depending on the time of day and on your level of activity.
In addition to clothing yourself, you need to think about your tent and your sleeping gear if you will be in the backcountry for a few days. If you will be in the park in winter, always, always bring a four-season tent. Do not depend on your 3-season tent to protect you in country where heavy snow and rain, as well as avalanches, define winter weather. Check your sleeping bag's temperature rating. Always remember that the rating is the lowest temperature at which a human can SURVIVE in that sleeping bag; it is NOT the lowest temperature at which a human will still be COMFORTABLE inside the sleeping bag.
Having the right gear ensures that your trip to North Cascades NP will be not only memorable, but also safe and comfortable.