Using figures from an example fridge in Thermodynamics (Cengel and Boles), the R134a is compressed from 140KPa to 800KPa in the compressor. This particular fridge would have liquid in the evaporator at -19°C, so I figure any ambient temperature lower than that could potentially cause problems. However, -17°C is the typical set point for a freezer, so I'm going to say the freezer would never turn on under such conditions, and this is a non-issue, at least for this particular example fridge.
Btw, the fridge in this example has a CoP of 3.9, excluding heat transfer from the refrigerant lines, any auxiliary energy usage such as an air circulating fan, and losses in converting electricity to torque. Which is to say, I have no idea what the typical CoP of a fridge is.
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