My wifes 07 punto is having trouble starting when temps are sub zero.

The car spins the starter no problems if just doesn't want to catch. Leave it a minute while scraping off the ice and it'll and run (sounding a bit sick) but die as soon as you press the accelerator or after 10-20 seconds if left. Give it another minute and it'll catch fine and work as expected for the rest of the day.

Seems to be no issue with the speed of the starter, so not obviously a battery problem.

Any suggestions before I find another dealer (the local one seems to have shut down).

engine ecu temp sensor faulty, or possibly crank sensor, i would be more inclined to go with engine temp

Temp sensor is the likely culprit

Just don't start back probing anything with a multi-meter on a Fiat, it is known to cause ECU failure at random times.

My good lady's punto used to do this sort of thing when the spark plugs were getting due for a change