Why doesn’t water freeze under a thick layer of ice? why the expression fur coat heats is wrong?

Because ice is less dense than water. And reservoirs usually freeze from the surface. When ice forms on the surface, it prevents further freezing of water deep into the reservoir. Although substances usually become denser when frozen, it is not ice.
The fur coat does not heat, it is only a heat insulator. It retains the heat of the body, and it is not a fur coat that heats, but a person’s own body generates heat. Clothing (any winter) acts only as a heat-insulating material.