Yes, WATER does freeze when WATER is at 32°F/0°C. (NOT THE SURROUNDING AIR) If it is sitting on a plate, or in a jug, or touching anything else, the mass of what is in contact with must also be at or below freezing. When water is in a puddle, and dropping the air temperature to freezing and saying the water has not turned to ice is not accurate. The water is not the same temperature as the air, because the ground is warmer. Same goes for putting something in the freezer... the water, and anything that is containing it, or touching it must be given a chance to reach the freezing point, before the water will freeze. If it takes 2 hours for a plate of steel to cool from 50°F to 32°F, the water will be drawing heat from the plate, until the plate reaches freezing - at which point, the water will turn to ice... I can put a 5 gallon jug of water outside when it is -40°C, come back in 1/2 hour and say - hey - water doesn't freeze at -40°C because this isn't frozen. Of course, I could put a 5 gallon pail of boiling water outside, but I didn't mention that part... it's all relative people. Anyone who lives near a lake will understand this. Overnight temps can dip well below freezing without the lake freezing over - because the WATER temperature has not yet reached freezing.
The REAL question is...
If there is a plane on a conveyor belt, and the plane has a sealed jug 1/2 full of water in it, and the conveyor can match the forward speed of the airplane exactly, but in the opposite direction, and the air temperature outside the plane is -55°F.... at what altitude will the jug freeze due to the wind chill if the plane can take off? (now we'll see who is paying attention)