Why do all the outlets freeze up and stop working at the car park?

If the outlets literally aren't working, first thing is to check whether the circuit breakers tripped on the panel. In unheated parking lots, protection systems often kick in because of voltage spikes or grounding issues, and that's easier to fix than dealing with ice buildup.

But if it's actually about icing and condensation, then yeah, it all comes down to temperature fluctuations. When cars are parked in the cold and then warm up, or warm cars come in from outside, you get moisture. The metal contacts on the outlets cool down to the dew point, and moisture just condenses on them. That can lead to contact oxidation and short circuits.

By the way, we had a similar situation at our parking lot - people were trying to warm up their cars in winter, and the outlets kept failing. It helped when we installed sealed caps on the unused outlets and made sure the lot was properly ventilated so moisture wouldn't build up. If it's your personal lot or you can influence management - it's worth talking about ventilation or at least putting protective caps on the outlets when they're not in use.

Cold itself doesn't break outlets, but what happens in unheated parking garages is this: during the day cars are parked there, the space warms up a bit, and at night the temperature drops sharply, causing the metal contacts to shrink significantly. I know someone who had a similar situation at their dacha with an electrical panel in an uninsulated shed - in winter half the outlets would stop working until the temperature rose again. On top of that, you get condensation if humidity fluctuates: moisture gets inside, the contacts oxidize, and they stop conducting current. Usually it helps to either clean the contacts, or replace them with outlets that have sealed covers and moisture protection.