LCD & Li Ion batteries at -40°C
Put some power resistors under your electronics, with a thermostat which will shut them down once you reach a temperature of +5°C or so. Remember to tell your customers that your device can take up to several minutes to start up.



Note that this will only help if your LCD and batteries are rated at -40°C storage temperature, since you most probably won't be able to keep the heating powered continuously.

You might consider providing some thermal insulation as @laptop2d suggested, but keep in mind that you'll have the opposite issue in summer when it will be hot outside and you'll struggle with dissipating extra heat from your electronics sitting inside a thermally insulated box.