It would need to be waterproof.
Frame it using 2xs Sheath the outside with 1/4 plywood with the exterior painted. I would have it shaped pretty much like a lean to, taller at the open end. . Use any old tarp for the liner. Maybe even use an old sheet as it would likely be nicer to the car's paint finish.
Where in E. Ct are you. I'll donate the old tarp and my supervising/design/criticizing skills.
I think getting a fairly airtight seal along the bottom is possible. Just lay a few batts of insulation across the ground at the opening. Drive right over it, it will pop back up after your tires cross it.