I had a problem with a line freezing in an apartment. I would have to use a hair dryer to thaw out the line. As far as I know it never sprung a leak. The only way I could keep it from happening was to run the water very slightly, think a dripping tap, to keep the water flowing/moving through the line on really cold nights. I cannot remember if it was the hot water or cold water line.
Good luck. I hope it works out okay.