In the case of HID lamps I would suspect fake or defective lamps as the most likely cause.
Other possibilities include wrong line voltage, wrong frequency, or excesive vibration if atop poles or masts in windy conditions.
A 240 volt ballast , or the 240 volt tap on a multi voltage unit, will over run the lamp on a 277 volt supply with consequent short life.
A 50 cycle ballast on a 60 cycle line will have a 20% higher impedance and under run the lamp which may shorten the life, and not extend it as one might expect.
Or of course they might be the wrong lamps for the ballast or fixture.
Over frequent switching can kill HID lamps, though induction lamps should be fine.
Cold should not be a problem in itself, unless severe enough to shatter the lamps.