If the cigarette lighter socket is turned off when the ignition key is turned off you can leave it plugged in all the time if you want.
If the socket stays live when ignition key is off, unplug the coolbox or you could flatten the battery.
Look on the coolbox for the amount of current drawn. Then find out the wattage of your car battery. Current will be drawn from the battery until it is exhausted and you won't be able to start the car. That is of course if the cigar lighter is permanently live as mentioned above.