I have two old R12 fridges in an unheated garage and there is a noticeable difference in their operation, summer and winter. But it’s nothing I’m concerned about because they are full of beer; but the temperature fluctuations I can tolerate for a bottle of beer may not be suitable for food.
So, you pays your money and you takes your choice.
There’s nothing to stop you putting your fridge in an igloo, if you want to, but it may not work as well as it would in a nice heated kitchen where it was intended to go..
But here are two plausible reasons why a minimum temperature limit is suggested by manufacturers and may affect the operation.
The first will be familiar to split air conditioning engineers as over condensing.
If the condenser is too cold there is a possibility of the refrigerant gaining too much sub-cooling, reduced condenser pressure and reduced flow through the capillary tubes feeding the evaporator. In other words, there will be a reduction in the machine’s capability to do its work. This may result in damage, long term.
Hydrocarbons (R-600 and the like) obey the same laws of thermodynamics as everything else. Their transport properties are selected to be close to the conventional CFC and HFC refrigerants. I like to watch YouTube videos of a similar theme when I'm looking for information about the right product.
