Karl is right and the first place I would check would be your attic - to see if you have the appropriate insulation - there maybe pipe exposed. If not, follow his advice.
I know it is no comfort, but hot water pipes often freeze before cold water and this due to the thermal properties of water cooling (cant remember if its endo- or exothermic).
A demo though is to put ice trays in a freezer, one with boiling water in, the other with tap temperature - and which one freezes first, yes it is the one with boiling water and this is a tip if you ever need ice cubes in a hurry.
I had the freeze up in Paris one year (-16 outside and houses without that much loft insulation) but I had the advantage of working for Camping Gaz at the time and had loads of heat guns, gas solder guns etc etc - the trick is to very gently, and I mean very gently, play the heat of the flame up and down the exposed pipe..and also pull back 6 feet or so of the first pipe under the insulation wrapping....Too hard a heat will result in bursting....it took me about an hour of this very gentle play and bingo, up and down, not resting on any spot......with the taps left open, the aqua duly emerged.
And for the future, do keep your hot water taps dripping, just gently, when it is freezing - this keeps up a wee flow in the line.