Leaving faucets dripping can and does prevent freezing of pipes.
However you should allow the faucet to run at a slow stream instead of just a drip as a faucet that is just dripping and now flowing at a small stream can more easily freeze.
Flowing water does not freeze as easily because when water is flowing the water molecules are disrupted and also the water is mixing constantly with warmer water and colder water.
The movement of the water and the disruption of the water molecules prevents the formation of stable ice crystals, which makes the water more resistant to freezing.
The constant mixing of the water when it's flowing also can bring warmer water to the surface and delay or prevent freezing.
Water also has an unusually high specific heat, meaning it takes a significant amount of energy loss for it to freeze.
Even when the air temperature falls below freezing, water needs more time and a greater, sustained drop in temperature before it reaches its freezing point of 32°F.
Flowing water can still eventually freeze if it gets cold enough or if the water is now flowing fast enough.
If you leave a faucet running on a slow trickle then it can freeze faster than the water would at a larger flow.
To prevent water pipes from freezing insulate the pipes and use heat tape and keep your faucets running at a slow trickle.
The freezing point of water is 32G but the movement of the water creates mixing of the water and water molecules which can delay or prevent freezing of the water, especially at temperatures that are slightly above freezing.
It's most common for pipes to freeze when temperatures drop to 20 degrees F.
However, pipes can technically freeze whenever temperatures are 32 degrees F or lower, but it takes much longer.