No reason to run hot water in this instance. The pipes freeze before they get into the house, when the water is cold. Letting the hot water run is just running gas down into the sewer.
Unfortunately the PVC piping to all of the fixtures is run beneath the house. There's a few inches (~4") of fiberglass insulation under the entire house, the piping is sandwiched between the insulation and the floor joists. Most of the piping is perpendicular to the joists, so it's not even sucked up against the sub-floor. Last time one of the broken lines was a hot water feed to the master bath.
The way I figure it, running the hot water not only keeps the water in those pipes running, it's also heating the immediate area, however minimally that may be.
At least there's plenty of room to work under there, relatively speaking. The crawl space varies from ~18" to almost 30".
I'd like to replace it all with PEX, but realistically, that's not likely to happen.