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.