Hello, i am afraid refrigerators are not designed to work on a low ambient temperature. Refrigerant is greatly affected by temperature so if the ambient temperature is lower than the compartment temperature, then the thermostat will always be off and the compressor would not run.
If the ambient is low. the refrigerant some how decrease also its volume since its temperatures lowers. hence, you would be have a temporary " lack of refrigerant issue" which would come back if the unit is placed on a much higher ambient temperature surroundings.
You can try to place the unit first inside the house and observe it for a few days. If everything works fine, then there is no issue, but if still there is a problem, then I would say the unit really has a problem.