First let's look at the things to be aware of with the camera itself:
It's easy to assume that like ourselves we need to keep the camera warm but actually this can cause problems with condensation which is really not very good for your camera.
As we are going from warm homes to cold outside temperatures and back again there is a danger of this occurring.
To avoid this acclimatise your camera to the cold by introducing it gradually - leave the camera in a car or garage for up to an hour before using it. Reverse when you return home.
You could use a ziplock plastic bag that you can seal your camera into. Any condensation should then be on the bag and not your camera.
Very low temperatures will affect the performance of your camera. You will notice this most with battery life and possibly the performance of your LED screen. Make sure you have a fully charged battery when you go out and, if you have one, take a fully charged spare that you keep in your pocket.
Have a cloth to keep snowflakes off your lens.
Now for taking great photos in the snow:
Snow creates a lot of extra light for your camera to cope with. This can result in much darker photos than you were expecting as the camera's settings attempt to deal with so much light. To compensate for this use your Exposure Compensation setting - set it to a plus figure. You probably won't need to go higher than +1 but experiment to get the photo you want.
Snow can appear blue in photos so use White Balance on your camera to overcome this.
Autofocus systems can struggle as they need areas of contrast to lock onto. Make sure you use the other elements in the photo for the focus system to lock onto - trees, fences, people, buildings etc.
Think about the colour in a snow scene. If you're shooting on a grey and overcast day you might want to think about black and white photos. If you can add a splash of colour - like the bright colours of the children with their sledges above, it can really enhance your photo.
Try different shutter speeds to capture falling snow in different ways. be aware of how much snow is falling and whether you are keeping your camera relatively dry (see my blog post on DIY rain gear on the website)
Think about details too - snowflakes and ice crystals make lovely shots if you're into macro.