There are many possible issues. A code read may give you a clue.

Worst case scenario is that the engine injected sufficient water to run hydraulic on one cylinder and has bent a conrod.

More likely:

The air filter is soaked. Remove and gently dry out.
The ignition leads got damp which is causing HT current to leak out (spray with WD40).
One of the sensors got drenched. A code read will give you a clue as to which. Again, WD40 or the carefull application of a hair dryer should sort it.

If you're lucky, the car will be as right as rain (ahem) tomorrow.

If you drive through deep puddles at speed, it will happen again. I know it's not deliberate, but....... Using silicon grease on HT contacts and sensors should help. About £8 from a motor factor, less on eBay.

A search should find Fiat ECU scan, with details of cables, etc. Alternatively, the car is OBD 2 compliant, so anyone with a code reader should be able to do it for about £25.

either the main engine earth straps (gearbox - Engine Bottom back - Chassis earth) are affected by moisture

Or the crank sensor would be my bet

but the exposed coils my worry possibly

Get the car dry and see if it improves

Ziggy

meh I used to do this all the time in early Mondeos because the engine air intake was so low to the ground, basically used to soak the air filter, like fingers said.

could be HT leads if you properly soaked the engine bay, puntos seem a bit sensitive in that department, but I would be doubtful of it being a sensor as they are all weather sealed and soaking the waterproof connector plugs even if water did get in it its unlikely to stall the engine.