I've heard that turning on faucets to a slight drip will prevent pipes from freezing, but I've never understood why this is the case. Can anyone out there help me to understand? Thanks!
Pipes are damaged when ice forms a complete blockage, and the expansion of water trapped by it puts too much pressure on them.
Now, ice is a pretty good thermal insulator, so once a little ice forms on the inside of the pipe further freezing proceeds slowly. If the water is flowing there will not be enough time for it to freeze between leaving the (relatively warm and protected) underground run and exiting the pipe at the dripping faucet. Thus the pipe never freezes all the way through, no blockage forms and excess pressure is never applied.
I would say it is a simple case of heat transfer. The new water (from the mains) is above freezing (usually by 10C or more), so the flow is transfering heat from the relatively warm input water. I would also say, that the opening through the end of the pipe might act a bit as a pressure relief valve, i.e. some freezing of the contents of a closed pipe means a major increase in pressure, however if you have it slightly open the excess pressure can be relieved.
Having said all that, I've seen how I can't use the garden on a clear morning with a temp less than roughly 40F. Radiational cooling of the hose at night, means some ice is present in the hose, and turning it on (with the hose nozzle present), usually just results in ice jamming up the nozzle. So I wouldn't count on your slow drip to not clog up with ice.