Good question! In general, this is not correct. Water freezes at 32°F, regardless of whether it is moving. In still water, such as lakes and ponds, the top of the water freezes first, and since ice is less dense that liquid water, it remains on the surface and insulates the rest of the water from the cold. The rest of the pond doesn’t freeze because the temperature of the ground below never reaches freezing. For example, in Wisconsin (my home state!) the soil temperature two feet below the surface never goes below 32°F, even in heart of winter.

For flowing water to freeze, the surrounding air has to be colder than 32°F, because the flowing water mixes with itself. So, the colder water on the surface mixes with the warmer water from the bottom, and the average temperature is somewhere between the two. Even so, if it gets cold enough, the mixing isn’t enough to keep the top of the river from reaching 32°F, and the river forms a layer of ice on top. The water flowing below, however, is still above 32°F, or it would freeze as well.

However, there are a number of additional factors that can influence the freezing process. If there are any dissolved salts or other solutes in the stream, the freezing point will be lowered. For example, the freezing point of sea water is around 28°F. Also, the motion of the water can cause heating. For example, water in a waterfall gains kinetic energy as it falls, which is converted into heat and sound energy at the bottom. Therefore, the surrounding air temperature would have to be lower to force the water in the waterfall to cool to 32°F and freeze.

Finally, the fact that the water is moving might influence the freezing behavior, but it would encourage freezing rather than discourage it. For example, if you have a very smooth, clean container of pure water (such as a store-bought bottle—Fiji Water seems to work well), you can sometimes lower the temperature to below the freezing temperature, because there are no places where ice crystals can start to form (called nucleation sites). This process is called super cooling. Then, if you shake the bottle or hit it on the table, you introduce some air bubbles into the water which can nucleate ice crystal formation, and the water will spontaneously freeze and become ice. You can try this at home by buying a bottle of water, and putting it in the freezer for a few hours, then carefully removing it before hitting it on the table to nucleate ice formation. In the case of the river water, the motion of the water, and the fact that the ground is not a smooth, clean surface, would prevent the water from ever becoming super cooled.