Up north I don’t have outside faucet problems until it is 15°F or less for 48 hrs, or inside pipe-next-to-exterior-wall problems until it is well below zero. But I understand why you are uneasy about it. And I probably have much more wall insulation.
It would be OK here except there is about 18 inches exposed in the pump house. I have an old heated wrap somewhere which should do the job but easier to just let the faucet drip.