What kind of vehicle is it? What type of fuel injection does it have? I assume it doesn't have a block heater? Are you pumping the gas pedal to try and start it?
If your killing the battery quickly, how quickly? Do you know how many cold cranking amps your battery has?
Seeing that you just bought a battery charger and it's getting colder, take the battery out of the car and charge it over night...inside your house where it's warm.