Recent freezes in southern states (Texas) have caused pipes to burst, as the pipes are not insulated for freezing weather. I believe that running the water can prevent the pipe from freezing.
Practical, actionable and measurable process is sought. I have witnessed uninsulated attic pipes burst because of a 3 day freeze in Florida in the 80's.
An opened faucet will already lower the chance of a pipe bursting.
The typical way a pipe bursts is when it is fully shut. Since it is watertight, there is no place for the water to go. When the water freezes and expands, the only way to go is the side of the pipe, so it bursts.
When the faucet is opened, even just a little, it allows the water to drip out. Now, you say, the water is frozen, wouldn't that still burst? The answer is no.
As the water freezes and expands, the kinetic energy exerted by the ice against the pipe actually melts the ice, and just enough will melt and flow out of the faucet. This is how ice skating works. The physical pressure on the ice creates a thin layer of water, which obviously refreezes immediately once the pressure is removed. You can also easily demonstrate this by using a knife on a block of ice. The pressure from the tip of the knife melts the ice, even though it is just as cold.
So with the faucet opened just a little, as the water pipe freeze over, you'll eventually see the ice "leak" out of the faucet. This is the water melting and freezing immediately. Even though the opening of the faucet will eventually freeze over completely, that frozen opening is still substantially weaker than the pipe, and the expanding ice will continue to "leak" out of the faucet and not burst your pipes.
People who use a tankless water heater, especially a gas-fired model, will be familiar with the "thermal sandwich" effect: when you're running hot water, shut it off for a moment, and then run hot water again you can expect a little burst of cool or cold water coming through the pipes a few seconds after the water flow is restarted. A small pocket of cold water is sandwiched between the hot water.
People who live in a warm or hot region, especially if they don't have central air conditioning, will have noticed that if one lets the cold water run a while the water temperature at the faucet abruptly drops when all the water that had been sitting in pipes in the building has flushed out and cooler water that had been sitting in pipe in the ground arrives at the faucet.
This same phenomenon could be used to test for risk of freezing:
If the measured temperature of the water drops to 32°F / 0°C then somewhere along its path it is beginning to freeze. Note that the water could be warmed in the piping somewhere along the way (after the freeze zone), so it might be appropriate to choose a higher temperature as the freeze-warning threshold.
One might anticipate a possible freeze, leave the water running to avoid that outcome, and then wonder whether the flow is sufficient. If the flow is stopped for a short time -- a minute, perhaps -- and then the temperature is tested as described above, it'll give good insight as to whether the flow had been adequate to keep the water (the pipe walls, really) all along the path warm enough to avoid freezing.
The answer, unsatisfying though it may be, is "it depends." It depends on the weather, and on the exposure of the pipes to the weather.
"Best practice" (from a cold climate point of view) is to have all the waterlines adequately buried below frost line in soil outside, and on the inside of insulation in a heated building, which they come into below frost line. Not very Floridian, from what I've seen when visiting the state, with pipes running outside walls and aboveground...
Our neighbors had an inadequately buried well pipe and ran water all winter to keep it open. It was a solid stream, not a drip, and even then sometimes they adjusted it a bit too low, or the weather got a bit too cold, and it froze up anyway.
Prognosticating the weather and turning the flow up when the temperature went down was something they worked to perfect, but still failed at occasionally. There may be times and temperatures where a drip would serve, and there will be others where a drip is not nearly adequate. Given lack of opportunity to practice and refine what your particular system needs, shutting it off & draining it fully may be your best option in rare instances of cold weather, unless you are going to change it to be more suited for exposure to cold weather.
Note that "running water to keep from freezing" depends on the source of the water being significantly above freezing - depending how much of your local water distribution system is actually buried .vs. exposed, that can vary - probably your groundwater temperatures are far above our cold climate groundwater (typically 50°F / 10°C), but if there are long runs of exposed pipe before the water even gets to your house, the incoming water temperature you see may be quite low in a freeze event.
If it's coming out warm enough to melt ice-cubes it's fast enough.
