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NO, bulk of the water is below the surface, and at 4C, because that is where the density of water is at it's highest. Then the upper layers cool down further, and as they cool down they float on the deeper cold layer, so only the top layer will eventually reach 0C, and being at the top, and lowest density, it will continue to lose heat by radiation, till eventually it has lost enough energy for the ice crystals to start to form, and grow to cover the top.
On the base of the container water will be 4C, the rest of the container is someother temperature between 0 and 100.
How does ice actually come to being if the water crystals circulate amongst water of a higher temperature?