Yes, you should let water drip from faucets when it's cold outside to prevent pipes from freezing and bursting:
When to drip
Drip faucets when temperatures are expected to be below freezing for several days. You can continue dripping until the temperature is consistently above freezing.
Which faucets to drip
Drip the faucet that serves exposed pipes, such as those in attics, garages, basements, or crawl spaces.
How to drip
Drip slowly and steadily.
Other tips
Open cabinet doors under sinks near outside walls.
Drain and protect water softeners from freezing.
Insulate hot and cold water pipes.
Keep your home at a reasonably warm temperature.
Cost
The small increase in your water bill for dripping is likely less than $1 a month. However, the cost of water damage from a burst pipe can be thousands of dollars.
When to stop dripping
If you lose power for more than 24 hours, stop dripping and turn off the water at the main shut off valve outside.
You can also watch this video to learn more about dripping your faucet during winter weather:
