I'll give you a definite 'It depends'.
I used to live in the Chicago suburbs (zone 5) and now I'm in NC (zone 7) Both locations I ran my pond/waterfall all year. Part of it depends on the design of your stream & waterfall - if the edges are low & there is a high risk of ice damming diverting water out over the liner, then I'd shut it down. If you're the sort of person who really doesn't spend much time outside in the cold weather, or you'd rather not have to keep a close eye on the pond, then I'd shut it down.
If, however, your edges are significantly high that you're not worried about ice build up, and you're OK with having to be out there every day making sure things are running properly (and actually dealing with any problems that might arise) then go ahead & leave it running.
I do keep a deicer floating right in front of my main skimmer & run it when it's so cold I'm worried about the water freezing up at the opening. I also keep a long hose in the garage, so IF necessary I can drag it out & add water (need an unfrozen hose)
I shut down one year here in NC because my pump died in very late fall & by the time the replacement arrived everything was already frozen, and, I did one year in Chicago have an exposed ball valve crack, so the pond had to be shut down mid-winter (pump pulled, bubbler installed) during a sub-zero stretch of cold - not fun. But other than that, I love having it run all winter. The ice sculptures are beautiful.