Amps is a measurement of instantaneous current, or power.  4.5A is equivalent to about 62 Watts (4.5A x 13.8V = 62.1W).  What you are asking about is how much energy it takes to freeze some quantity of ice.  Energy can be thought of as power over time.  In this context it is generally measured in Watt-Hours.  So, the fridge, running continuously for an hour, would consume 4.5 Watt-Hours.  I don't know how much ice it would freeze over that time, but some other reader might have tested this.  In any case, once the ice is frozen, the fridge merely needs to keep up with heat leakage through the insulation.  In my experience, this is about 5 minutes of operation per hour.  This equates to a 4.5A x (5min/60min) = 5.2 Watt-Hours / Hour.  This means that once the fridge is cold (done while driving), you can leave it on for long periods (full day) without much concern.  I should look at the 4.5A number because it now seems high.  I've left the fridge running for more than a day.  Theoretically, that should have killed my battery, which it didn't.

Note: don't just fill the bottom of the fridge with water and let it freeze.  The expansion will kill the fridge coils.  Always put the water in jugs and then let them freeze.