Thought I'd chime in since I have a fairly shallow stream (only about 10" deep) that I keep running all Winter... I've never had a problem with the stream freezing up and diverting, and I rarely put heaters in my pond except when it is bitter cold out (like below 0F). What I have noticed is a top layer will form ice over the stream, and it sort of caps off the water. The water will continue to flow underneath the ice, and the warmth of the water seems to prevent the ice from getting thicker. Something about flowing water preventing the build-up.
Keep in mind that with my weather, I rarely see the stream iced up more than 2-3 weeks at a time, then it melts again.