Hello; Fish do make their way into the deeper pools and portions of a lake or pond. There is less current to deal with in a deep pool of a river so less energy is needed. The water freezes from the top down, as mentioned, and a deep area will not freeze.
In lakes and large ponds there is a layering of the water with regard to temperatures. In the winter the surface layer can be colder than the deeper levels. This lasts untill spring when increased sunlight duration raises the surface layer temp to near equal of the bottom. The lake then does an overturn of the water during which the nutrient rich deep water is churned and mixed into the surface and the lake has similar temps throughout. This coupled with the increased daylight produces an algal bloom which charges the food chain. There is also a good mix of dissolved oxygen throughout the levels of the water allowing the biger fish to stay in the shallows. This is often the best fishing period of the year. By summer the upper layer becomes much warmer that the deeper levels and will hold much less oxygen, so the bigger fish can not spend much time in the shallows. By fall the upper levels cool down and another turnover happens with a second bloom and the next best fishing period.
There is also a thermocline layer that forms about 10 to 15 feet except during the turnovers. If you have ever dived deep into the water during the summer this thermocline layer can be felt.
Fish also have different levels of energy needs as the water gets colder. I believe their metabolism slows down as the temps drop.
There is also the possibility that the fish blend in so well that they are still present but cannot be spotted. They will get in behind a boulder or in a pool in a creek where the current is much slower and just hover with little movement. I have tried wading in creeks during winter in very clear water in the Smoky Mts and could not see fish untill I spooked them.