No, water supply pipes will not freeze if they are actively dripping. Allowing a faucet to maintain a steady, narrow drip (about one drop per second) keeps water moving continuously through the supply line. Because moving water requires a much lower temperature to freeze than stagnant water, this continuous flow prevents ice crystals from forming and expanding inside cold pipes. Verification: Check that the faucet maintains a steady, thin trickle during sub-freezing nights.
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