1: Snow creates a fundamentally unique lighting situation that requires extra exposure care. First understand that the exposure will easily be one stop brighter than the same scene would be on a normal sunny day without the snow. It's because of all the light reflecting from all those snow-covered surfaces. Second, understand that all that snow on the ground serves as a great fill light—so you're going to have naturally high-key scenes and you'll have to look for special circumstances if you want to create something dark or dramatic with light. And third, because of all that bright snow all around, your camera's light meter is likely to be fooled. It's going to be confronted with a scene that is full of bright and white tones, but it's going to try to expose for them as middle tones. So manual exposure shooters have got to pay special attention not only to keep from blowing out highlights on bright and sunny days, but also to be sure your camera's meter doesn't turn that same snow into a gray, mediocre mess. Adjusting exposure compensation to +1 is a great shortcut to keep auto exposure shooters from turning out frame after underexposed frame.
2: Find the edges of light. If you can find areas where your point of interest is in bright sun but framed against a dark background (a skier in bright sunlight with the shadow from a tall tree forming a dark background, or set off against a deep blue sky, for instance) you can make your subject practically pop off the page. Better still, position that subject so that the sun is working like a rim light (hitting the subject from behind) and you'll really enhance the illusion of depth. The edges of transition between shadow and highlight offer great opportunities to add interest to snowy day photographs, whether you're framing a bright subject against a dark background, or vice versa. One point of warning, though: don't allow your subject to be in mixed lighting in this scenario—say, dappled sunlight falling on your subject's face. The extreme contrast of bright sun and dark shadows can ruin an otherwise wonderful image when they're competing for attention (not to mention the correct exposure). If you're faced with such a situation, expose for the highlight and fill those dark shadows with a flash.
3: Look for low light. At the end of the day (or, if you're a better man than me, at the very early beginning of it) you can find some beautiful low light. When shooting on snow, something special happens as the sun sets: first the raking light enhances shapes and textures, and eventually the blanket of snow starts to reflect the glowing sky and taking on the beautiful blue color. Suddenly instead of a surface that's glowing bright white, snow becomes a beautiful blanket of color beneath dusk (or pre-dawn) light. The benefit, of course, is that the snow still serves as a reflector, so you get the added illumination of all-over fill that makes it a little easier to shoot in low light. If you can't wait until sunset and you don't care to rise before dawn, you can still find blue, soft, lower light in another snowy situation at any time of day: open shade. Look for tall trees or other areas that create the open shade that's perfect for portraits—and many other purposes too.
4: Break the rules of composition. Sure, the "rule of thirds" and "S curves" are appropriate any time of year in any weather, but something happens when you're working with a snowy scene: the earth itself becomes a blank white canvas—and that lends itself to photographs that use symmetry and geometry and even repetition of simple patterns for interest. A plain old tree may look like nothing special in a summer field, but when that field is blanketed with snow and the tree is isolated against a background of blue and white planes, that tree can make for a great photograph when it's centered in a geometrically symmetrical composition. Snow evens out the inconsistencies in the landscape and simplifies it, and that simplicity really lends itself to photographs that play on isolation, balance and symmetry. So use it while you can, before the snow melts and you're back to following the traditional rules of composition.
5: Keep yourself and your gear warm and dry. (I know, you read this in every winter-related story you ever see. But it's serious stuff, because it's no fun ruining your equipment or shooting in misery. So bear with me for just this one tip.) I like to treat even dry days in snowy climates as if I was shooting on a rainy day—keeping my gear in dry bags with waterproof enclosures in order to prevent snow from sneaking into the kit and leaving moisture in the lens. When I take that gear inside warm up, I keep it in a tightly sealed plastic bag to allow it to come up to room temperature without condensation forming on the equipment itself. (The reverse also holds true; let your camera cool down before pulling it out of the bag when it's time to start shooting or you'll get fog on—or even in—your lenses.) When it comes to keeping myself warm and dry, I don't mess around there either. I have too many memories of a younger me thinking "Oh, it's not so bad out there," only to have a hard time making photographs because I'm so distracted by my discomfort (cold, damp, or both) and all I can think is, "Can I go back inside now?" This is not a recipe for success. Don't skimp on protecting yourself or your gear when working in snow. One bit of advice: pay special attention to hands and feet. Cold fingers and cold toes are the quickest way to end a shoot prematurely.