Cold does not kill bacteria. If you unplug your freezer and let the food sit in there for a few days it will rot. Cold only slows down chemical reactions which slows down biological processes. Microbial cysts can be frozen and brought back to life when conditions are favorable just like seeds. The same is true for some invertebrate eggs like flies.
Neither cold air nor warm water kill bacteria. Cold helps preserve food by slowing the growth of bacteria and fungi that will spoil food. We use warm water to wash our hands for an entirely different reason, which is just that it makes it easier for the soap to remove dirt and grease from your skin. Soap also doesn't kill bacteria unless it's specifically antibacterial soap, it just remove the bacteria, oil, and dirt from the surface of your skin to get rinsed away by the water.
Cold slows down bacterial grow, it does not kill it.
Bacteria doesn't just live on our skin, it lives in dirt and oil on our skin. Warm water is better at dissolving, softening, and removing dirt and oil. It isn't about killing them, it is about sending them down the drain.
Its easier to get dirt, grease, oily things etc off your hands with warm water. Its not to kill bacteria, thats what the soap is for.
(As far as i know)