Sorry to disagree regarding a fault, but many manufacturers vehicles suffer with this problem, not just Fiats. The basic problem is due to water freezing the linkages, keep the water off and there is no problem. Unfortunately because alloy wheels are the norm now (with big gaps in them to help air circulate) this exagerates the problem by letting everything cool very quickly once parked. The multipla also has another part of the linkage exposed so does suffer slightly more often than other vehicles.
The easy answer is to keep the car parked in a garage overnight, or park the vehicle in gear (1st or reverse depending on which way the car is likely to roll) with the handbrake not applied, and also a little oil or grease on the linkage would also help repel any moisture.