I think you should remove snow, especially the exhaust pipe while you're using the heater. Take advantage of the heater while the motor is operable to dry any damp clothing. It should be a temporary shelter because any non-running vehicle is a heat sink.

Then you build a snow shelter outside of the car and the road and of course you should remove the snow, you may need the tires as emergency fuel for a fire. Note that it's best to add tires to an already burning wood fire. And you can use the vehicle's seats and cushions to use as insulating pads for the inside of a snug snow shelter such as a snow trench. Learn how to build them.

Also carry a winter sleeping bag and two Evazote pads for each members and make sure to keep them in the cab rather than the trunk where the vehicle is coldest.

Some snow house designs have a cold air well. Snow is a good insulator and the Canadian soldiers are even taught to use snow to shield against heavy machine gun shooting in the Bay James, you'd be surprised. (They are taught the art of survival in subarctic climate by the Cree Rangers as a step towards defending Canada's sovereignty of the Northwest Passage.)