Living near the Canadian border in upstate NY, the hot water line almost always freezes before the cold water line.
Try leaving the cabinet door under the sink open to get more heat into that space. The lines MAY be inside the "living space", instead of through the underbelly, from the bathroom to the kitchen (mine are in my Prime Time Avenger) so removing the access panel under the shower may also help. A hairdryer moved along the length of the pipe can speed things up and help get heat to the frozen section. Given the pipe is plastic, not metal, I'd probably stick to a low to medium setting. It will take longer, but I'd less likely to damage the pipe. The newer pipes are less likely to burst from being frozen, but be sure to watch for leaks when it does thaw. Good luck and keep us posted.
One final thought, if you are using an electric space heater to help heat the living space you may not be getting enough heat in the underbelly as the furnace won't be cycling as often it as long.
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