I mean, what kinda dripping are we talking here? If it's 5 degrees outside in an area not used to such temperatures, you should be running the tap furthest from your source (if not multiple taps) with a low stream -- not dripping. Moving water doesn't freeze as readily; that's a physical fact of nature, bruh. Yes, your water bill will be higher, but it'll be a hell of a lot cheaper than having your walls and floor torn up to fix a disaster.

But is your shit still gonna freeze even with streaming taps if a random cold snap takes us to -10? Yeah, probably! My pipes froze this morning in the 5-degree bullshit despite dripping (but not streaming!), and I unfroze them with a space heater under the kitchen sink at a 2/10 temperature setting.

Edit: More cold pro tips for anyone scrolling by:

• Keep your sink cabinets open (if you're not doing the space heater thing). Let your house's conditioned air get anywhere pipes are.
• Buy insulating foam pipe wraps from Lowe's (fuck Home Depot) and get them on all the exposed water pipes you can find in your crawl space.
• If your heat pump can't keep the place sufficiently warm, turn on aux/emergency heat and give your pump a rest. It'll run constantly otherwise, and depending on its age and the type of refrigerant, there's only so much it can do.
• Space heaters on indoor pipes (under sinks but also at your water heater) can conduct that heat through the pipes' run into your crawl space, lessening the chance of freezage.
• Replace your rotting half-inch plywood crawl space door with something that has weather stripping and some kind of backing.
• Replace your crawl space vents with ones that actually seal up nicely when closed. If you can see light through or around them when they're closed, they can be better!
• Know where your main water shutoff valve is; if you're in the city, this may require a water key, so get one!