Usually it means theres a fault in the cold star system, this can either be a Glow plug thats worn and needs replaced or something like the control unit. Fiat can do a diag and tell you whats what, however this costs. 99% of the time its a Glow plug that needs changing, although from what i hear some are a bugger to get too.
Now i'm confused about what you say about your light, does it do this:
Select key to first click (glow plug symbol lights up) wait for it to go out and start.
Then 10sec it comes back on flashing for how many flashes?
It shouldnt flash for more than 1 min, from what others say.
Mines is on in my Punto JTD and i had a diag as it was in anyway for one, and i've got 2 glow plugs out, it starts fine and will do untill i get them changed (this week), or more fail. However if the light is on for 200miles something is wrong.
Have you been letting the glow plug light go out before starting?