First, you want to get the right background. Leafless trees standing in a thick woods will do; shooting against a whitish overcast sky will not be as effective. Dark buildings or bridges as structures provide interest and enough contrast to catch the snow.
Another issue is shutter speed. The faster the shutter, the more it will freeze action. It depends on the kind of look you want. At 1/60th of a second, you get mostly distinct flakes as tiny round objects, although some may be bigger and slightly blurred as they are in motion. I have tried even faster shutter speeds, but if the flakes are too small and you freeze them in motion with no movement, you may not see them. At 1/13th of a second, you can still manage a hand-held shot comfortably and keep the image sharp, but wind-blown snowflakes will streak and blur a bit, making them longer, if not larger. In the two images below, the first was shot at 1/60th and the second at 1/13th. Judge for yourself which you find more effective or pleasing.