natural look and flow use fast shutter speeds.
For the stream flow, low volume and lots of movement around boulders and logs has a more pleasing effect than a flat river. Pleasing shots usually show the stream flowing past the camera (across the stream) or as the water flows towards you shooting up stream. Flat river shots are great with sunsets, etc.
When it is raining or snowing, speed up the shutter speed to catch the raindrops or snowflakes. Use a slow shutter speed to make the rain or snow streak across the frame. Keep your equipment protected from water by using an umbrella or camera raincover.
All photography is in the eye of the beholder.