Hello Denise,
I it is not absolutely clear from your description what type of cooler you have. You say its an absorbtion type, in which case it can be run from mains power, gas or 12vdc. 12vdc is only realy practical when you are using it in the car and the alternator supplies the quite high current demands, at other times Mains electricity is best, or in a well ventilateed area the gas input can be used.
If you box does not have mains or gas inputs, then i suspect you are refering to an electric cooler box. These use a clever semiconductoor chip called a peltier device. They run on 12V dc only. They tend to use quite large currents (4 to 6A), and becuase of that they will flatten a battery quite quickly - hence thier need for the engine to be running.
Becuase the cooler needs a certain amount of power typically about 50 Watts it must have a 12V supply cpable of supplying that amount. A draw of 4 to 6A on a battery will fleten it quite quickley, but many of these cooler boxes are supplied with a power supply that takes mains nd produces 12V for running the box. (see your caravan dealer or Maplin electronics. Make sure the power out put has morw curent than the box needs)
Because Watts = Volts x Amps, then it is easy to work out what the current needs will be for 12V and mains
50W = 12Vdc x 4.17A
50W = 230Vac x 0.22A
Mains is the better solution using a power supply to convert 230Vac to 12V dc.