Do not operate the LCD at these low temps, even if the other parts survive it the power supply and downstream circuitry is not designed for this and may easily be instable which would at best make it inoperable or at worse put instable power into the circuits.
These temps are bad for more than just the monitor. I recommend you install a minimal heater (or equivalent, like leaving an incandescent light bulb or two, three, as many as needed, on to keep the temp higher than freezing, or of course just set the thermostat so it never gets that cold instead of turning the heat completely off.
On the other hand, another possible solution is to just leave the equipment turned on, if it doesn't get much below freezing then the proximity of the screen should keep it warmer due to the heat in the back of the display. I think I'd leave a light or two on before being totally confident in that since I dont' know the environment, and since heaters or lights are not foolproof, a note and education of anyone potentially using the equipment that it should be brought up above freezing before being turned on (which doesn't mean look at the thermstat and turn it on when that says 1C, it means the insides of the equipment will be heating slower than the room air will so unless you're going to be scientific and measure this, a fudge factor is needed, say being at 10C for several minutes or something like that as a random guess, but we don't know just how cold it could start out in the worst case scenario).
Note this also means an ATX computer should not be left plugged into live AC if it can't be determined that both the supply internal temp and the computer internal temp remain above freezing, and the same may apply to other misc. parts though digital electronics and high precision mechanical devices will tend to be more susceptible to the temp.
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