Last week, we had a night that got down to -18F. In the middle of the night, the cold-water pipe going to the kitchen sink froze (but luckily did not burst). After some investigation, it turns out it froze where we had a dryer vent installed. The vent comes in between two floor joists, right where the sink's cold water pipe turns up and goes to the sink (see attached cross section image). The installer had removed a bunch of insulation from the bay between the joists, and not replaced it. The pipe is about 5" inside of the rim joist on the outside of the house.
To remedy the problem, I insulated around the dryer vent pipe, and put about 4" of fiberglass batting insulation on the inside of the rim joist (the thickest insulation that would fit between the cold water pipe and rim joist). I also wrapped the copper water pipe in foam pipe insulation.
Tomorrow night, it is supposed to get down to -30F. Does it sound like I've insulated things enough to prevent freezing? Would it be smart to shut off the main water supply, and drain the pipes for the over night, or can that cause other issues? Any feedback would be appreciated.