The compressor unit is just too big and heavy for that. COP is too low for Peltier cooling elements(aka Thermo-Electric Coolers). First generation of those will

The compressor unit is just too big and heavy for that. COP is too low for Peltier cooling elements(aka Thermo-Electric Coolers). First generation of those will be/are based on regular ice of H2O or a frozen coolant pack with some engineered high temperature ice; H2O is going to be more convenient since they can be drank and replaced.