Y'all are not helping me decide what to do..........
haha! You're right... except to say you really need to know your own pond and decide from there. Analyze your setup and your risk and decide from there. Our first winter we shut the whole pond down... then I worried all winter "what if there's water left in the lines... what if they freeze... what if my fish die...". Come spring, we turned it all back on and all was well. Until I realized that turning the pump off allowed our water level to drop down below the level of all my marginal plants and every single one of them died from being exposed to the elements all winter long. That was an expensive mistake.
We did a lot of research that spring and summer to figure out a way to keep our plants covered when the water level dropped - maybe use burlap, or straw, or put pots over them to protect them? Finally it hit us - why not do what nature does and keep the water (ice in this case) level high enough to protect the plants? That was the winter of 2013 in Chicago - 4th snowiest on record and 3rd coldest in history. A true test for our young pond. It survived. We survived. And we've never looked back.
As for your real question - beneficial bacteria... I don't know. My assumption is there is bacteria that dies in the cold, but there's also bacteria that survives. Maybe some even prefers and thrives in the cold, I don't know that for a fact. I will tell you this - we have observed algae that will be growing on the rocks BEFORE the ice even melts off the pond. It's a type of algae that we only see at that one time of the year. It's a beautiful, bright green and the fish will slowly come to life and devour it as their first food of the new season. Nature adapts. We appreciate it!