Last month when we had our first sustained below zero temps in 20 years, I did a diary about how I had read on a .gov site that one could just turn off the water and open all the faucets to prevent bursting pipes. I asked the dear Kos community if anyone else used that method instead of letting the water run all night. I had one guy who said he did it that way and fifty people who said "Don't do it". So, of course I did it. And it worked.
I was fascinated by the concept because I thought "You've been looking at this the wrong way". The pipes burst because it's a closed system. If a pipe freezes, it becomes like a hydraulic system. The pressure of the expanding ice on the remaining water will find an outlet which will be at the weakest point of the system, not necessarily where the freeze happened.
This answered a lot of questions in my experience with frozen and burst pipes. Like "Why did it freeze and break there?". It didn't, it froze somewhere else, the expanding ice pressurized the remaining water which broke out at the weakest point.
The point being that a frozen pipe will not break if it can transfer the expansive force along its length.
So on to the ultimate test. Friday I came home to no heat. After doing the usual manly tinker with the furnace myself, then call in the local he-men to tinker with me, we finally gave up and called a pro. By this time it was too late of course, but I did get a nice guy to stop in and say, "I can't get any parts til Monday, your board is fried; so you're screwed".
So I shipped the son off to my sisters, got out the two electric and one kero heaters and settled in for a long winters night. Temperatures Friday night were heading for the low single digits. I shut off the water and opened all the faucets.
I woke up Saturday morning actually sweating. Too many blankets and sleeping bags. It was 5 degrees outside. I walked into the bathroom to turn off the faucets and I could see my breath. I went down stairs and turned on the water; shat, showered and shaved; and sat there with my morning coffee feeling quite smug.
Results may vary but I say that you do not have to let the water run all night.