Many, many times I have heard from people how they photographed something during a snowfall and it turned out really dark and the snowflakes were not visible.
First of all, your camera turns everything medium gray because that is what a meter does. So to turn the snow white, go to the compensation dial and plus up the exposure to overexpose the scene. This will make the snow white.
Secondly, if you want to stop snow flakes, you must shoot with a high shutter speed. I prefer at least 1/640th of a sec or higher. This fast shutter speed will stop the flakes in mid-air before they drop.
Thirdly, make sure you place the snowflakes against a black or dark background, otherwise they will blend into the background and not exist.