Traveling from Milan to Umbria are gas stations open on Christmas Day on the autostrada
You mean you need an old-style manned station to completely fill up the tank before dropping the car off? Otherwise automatic pumps are always open in EU.
On the highway the gas stations are always opened 24/7. In general the most of gas stations in Italy nowadays have the ATM machine, so you can self service and refuel at any time, paying cash or with credit card.