Shooting a snow storm doesn't look that pretty because there are no contrasting colours - everything looks rather monotone in grey or white. You need something in the foreground that stands out against the snow, something with good colours.
Wait till the sky clears and the snow stops falling and now you've got a crystal blue sky to shoot against. If the sun is refusing to come out then it can help if your subjects are brightly dressed. Scarves are a great way of adding a dash of bright red or green into the picture to offset the white backdrop.
Birds are also a good source of colour, but only the right bords. A gull, for example, will not photograph well in snow as there is no contract, however, a robin will be excellent. The red in its breast will stand out really well against the snow.
Picking something with a bit more colour can really help pop the image.
If it's still snowing and you want to get a shot of some snowdrops, a good trick is to use something dark in the background like a holly bush. This way the white snow shows up really well against it.
Shooting white on white makes everything look like a blizzard.
One of the most important things with snow, which many people have a lot of difficulty with, is making the picture look like what your eyes are seeing. Your camera is going to get really confused by the snow. You can use a "snow" scene setting if your camera has one, else just notch up the exposure compensation on the camera. If the subject is too dark against the snow then +1 should do it. Don't worry if the snow overexposes a little, it can add to its look and stop everything from looking too grey.
Another approach is to change the camera's metering mode. By default, most cameras are set to centre-weighted where they consider the majority of the scene before making an exposure. There are also partial and spot metering options that consider only the centre and the pinpoint centre of the shot respectively and so will base an exposure on this area. If that's where your subject is, the exposure will be set accordingly and you probably won't need to adjust the exposure compensation.
One of the best rules for photography is the rule of thirds, which means you section your image up into a three-by-three grid and compose your image along the lines. This rule applies to all photography.
You can also change your perspective. Shooting a snowman by lying on the floor will give you a sense that he is far bigger than he is. Likewise when it comes to shooting a snowball fight if you're photographing kids - get low. If you're feeling brave get them to throw snowballs at you just as you take the picture... just make sure your camera's up to it!
Packing the Right Kit
If you're venturing out into the woods or city it might sound obvious or even silly to say, but wrap up warm. Take a blanket (for lying on), gloves are essential to avoid cold hands and wellies can be useful to avoid wet feet.
Also, make sure you've got a full charge in your camera's battery and carry spares. Batteries don't last as long when they are cold so you're likely not to get quite as many shots out of one.
Just like a car windscreen, camera lenses can also steam up when removed from warmer bags. The subtle changes in temperature can cause the lens to fog up so also pack a microfibre lens cloth to keep your lenses clear and clean.
A tripod is a useful piece of equipment for all landscape photography, and essential if you are photographing around sunrise or sunset. One fun thing about snow is that you can always "build a tripod" out of it rather than a snowman so at least that's one less thing to pack.
If you're walking through the snow you won't always want your footprints in the picture, so think about where you want to take your image before you walk into the shot. This way you've got the pristine snow without your footprints in it.
Finally, wrap up warm - I've been out on shoots in the snow before and it can be very hard to keep at it!