Below 6°C, there is a slow increase in hardening of olive oil as the temperature is lowered. At 2°C, olive oil has more or less the consistency of butter at room temperature. At -10°C, it is hard enough that a fork cannot penetrate it.
Chilling or freezing olive oil does no harm and the oil will return to its normal consistency when warmed.
On the other hand, the oxidation process (which is responsible for the degradation of flavour) increases with temperature. Keeping oil at low temperature is a good practice.
In fact, it’s so good that a patent has been issued for a method of freezing olive oil so that it retains its original properties. Why not serve your best olive oil frozen, like butter? That’s what Costas the Greek suggests in his blog!
Cloudy Frozen Olive Oil by John Deane.
Preserved Olive Paste, WIPO (WO/2008/122320).
Frozen Olive Oil and Six-toed Cats, Costas the Greek blog.