RedDwarf wrote:

I'm wondering if I have to worry about my pipes freezing below the
slab/under the house.

No. The earth is a tremendous heat sink.

On a very cold night, stick a thermometer in the ground, say six inches
deep.

I'd be astonished if it read below 50°F. In fact the reason a "trickle" of
water works to prevent freezing is that the technique brings warmer water
from underground (i.e., 50°) into the system.

As to "wasting" water: A minimal stream will "waste" about four gallons of
water per night, about the same as a low-flow shower (less than one cent).
An average bath uses about 30 gallons, an old-style commode flush uses six
gallons.

So, if you can avoid one flush per evening, you're ahead of the game. If you
can persuade your girlfriend to forego her bath by showering instead, you
can "trickle" for a week on the "savings" from one bath.