you can't really get the blurry effect with water that's not moving, and to do it, you need a long shutter speed... with water this still, that'd be several seconds. given the light, you'd need a neutral density filter and a small aperture to cut down the light enough to let the shutter work. closing the aperture won't "offset" the longer exposure shutter.. it will help cause it. however, a loooong exposure with snow falling would give you some pretty long "tracks" from the snowflakes as well.
the flash wouldn't do anything except light up the snowflakes.
don't expect to get much when it's actually snowing... the light is usually dull and flat, the sky will usually blow because of the long shutter speeds (unless you use a grad ND filter, and then you'll just get dark gray), and the whole image will generally be pretty drab. if you can get out after the snow stops, preferably on a day that's not completely overcast, you can get some great shots, as long as you're careful not to let the snow itself blow out...