Yes, that’s right — warmer water rises (that’s why there is, for example, a heating spiral at the bottom of a kettle). In addition, this phenomenon works with all fluids (i.e. liquids and gases). This is due to the fact that with increasing temperature, the density decreases and due to gravity, the denser fluid falls and the thinner rises (in the state of weightlessness this phenomenon would not take place). 

But water, unlike other fluids, has a peculiarity — in the range of 0—4 °C, it behaves the other way round — that is, as its temperature decreases, its density decreases. We call this peculiarity (originally) the water anomaly. In the temperature range 0—100 °C (i.e. in the liquid state) water has the highest density at 4 °C (exactly at 3.98 °C). When cooling water in a pond, nothing special happens up to 4 °C, but at lower temperatures the temperature distribution in the pond is different — at the bottom the water is 4 °C, while at the surface the water is at a lower temperature (because it has a lower density). Because the water is at a lower temperature at the surface, it may begin to freeze at sub-freezing temperatures, while the water temperature is still 4 °C at the bottom. Thanks to this strangeness, the pond freezes from the surface and fish can survive at the bottom. And we can skate on the frozen surface in winter. In addition, the ice thermally insulates the water below, so the pond freezes more slowly. Which again simplifies the survival of the fish. 

If the water did not have this property, the fish would have a hard time surviving the winter and we would have to buy neoprene trousers together with the skates.