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Turning the fridge off at night to save energy does in fact the opposite: you waste energy. Because the power needed the next day to cool it down to normal temperature is more than the energy needed to keep it at the right temperature during the night.
With solar panels, it's a little different. They don't work during the night so you have to use power from the batteries. The next morning, the solar panels deliver power which partly goes straight to the fridge and partly to charge the batteries. The charging+discharging of batteries is less efficient than directly feeding solar power to energy consumers.
In short: your fridge will consume more power when switched off during the night but you might re-gain that if your solar panels deliver enough power in the morning when you switch the fridge on again. But better check if the panels deliver enough that early in the day.
The other side is the food in the fridge. More deviation to higher temperature means that it spoils quicker. Throwing away spoiled food is also a waste of resources ($$$) so it's better just to let the fridge run at night.
cheers,
Nick..
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