Extreme cold: Pipes seem ok, except hot water for bathtub which only trickles, despite being closest to water heater. Can it be frozen? Burst?
If it's frozen the water will not trickle.  It may be PARTIALLY frozen in which case running the water should eventually melt the ice and clear the line.  Run it slowly so that you don't dislodge the ice and have it block elsewhere.
Any water that is running in your pipes will be &gt; 32F (0C) and should melt any ice it runs past.