Why does all the water in lake have to be cooled to 4c before surface water can be cooled below 4c?

Water is most dense at 4 degrees Celsius. When cooling the surface water below 4 degrees Celsius, the colder water sinks because it is denser, causing a uniform temperature to be established at 4 degrees Celsius throughout the lake before further cooling can occur. This uniformity is necessary to prevent a temperature gradient that could disrupt the natural mixing patterns of the lake.