Hello Kenneth,
Even the fairly cheap and low powered 12V cool boxes consume at least 1.5 to 4A, continuously. This will be a significant long term drain on the battery and 12V systems.
Most of these unit also have a fan running, which can surprisingly annoying.
Whilst I appreciate they are more expensive, but have you considered one of the three way fuelled cool boxes. I think Coleman, electrolux and others do them. They are quiet, and they do a better job of keeping things cool.
I have one and when I'n not caravanning, I have it in the house to keep milk and other soft drinks in.