John, although I've been trained as an Ice Rescue Technician and practiced ice rescue on local ponds, I've never had to put that training into effect in an actual situation. No doubt some agency would be requiring the removal of a vehicle under the ice. I would suspect that they would mark the spot with GPS and have to return after the ice is off the lake to remove it with divers, air bags, barge and a crane. When we had a vessel sink in Lake Stevens two years ago, the vessel was lifted via divers using air bags to bring it to the surface and then towed the predominately submerged vessel to a launch ramp for removal. Most likely by the time that vehicle is removed after ice melt, any oil/fuel will have spilled out into the lake.
Fellow C-Brat Chris (the owner of "Scout") is a fire fighter in Wisconsin where they have lots of ice formation on the lakes and I know he has been involved in actual ice rescue. Perhaps, he can shed some valid first hand experience in answer to your questions.