You can get dry ice from most ice supply stores. Some theatical supply houses might carry it as well, or you could check with a local community theater or college drama department, they might have a machine to make dry ice.
The problem with using dry ice, however, is that you will need a bucket of water to put it in, AND more importantly it will creep down the sides of the car, and not really look like it should.
You could get some smoke bombs, I used some 'military grade' smoke bombs to great effect last april, they lasted 1 minute each and put out a LOT of white smoke. They're quite safe too, you can actually hold onto them whilst they burn, because they don't burn hot on the outside.
Thirdly, you could use a fog machine, which with Halloween basically right around the corner should be fairly easy to find. Theatrical supply houses sell them, as do many magic shops... If there's a halloween or costume store in your area you could get one from them. Walmart carries them as well, but I don't know that they've started stocking their halloween merchandise yet. The drawback to these is that they need to be plugged in, and they draw a fair amount of power, so it's not something that could be run off a power inverter.
I recently picked up a propane powered bug fogger, which you can fill with the same 'fog juice' the plug-in style fog machines use, and create fog that way, but unless you've got someone hiding behind the car puffing it out it might not work for you either.
Of all these options, I would recommend either the higher grade smoke bombs, like I used (just be sure you get enough, we ran through the 10 we had pretty quickly and had to resort to a PA puffing smoke from a cigar in front of the lens) OR the bug fogger filled with theatrical fog juice (martin, gem, or american DJ brands.. they all should work, I am currently using Gem)
I picked up my bug fogger for about $40 on sale at one of the large hardware chains (Menards is where I got mine, but Home Depot, Lowes, and Fleet Farm should stock them as well) and it uses the same small propane canisters that you use with coleman (or similar) camp stoves and lanterns. A gallon of the fog juice cost me just over $20, and is enough to make a LOT of fog/smoke effects... so... for about $60-100 you should be set for fog for probably a year or so, maybe more, or less depending on how much you use it.
I'll see if I can't dig up a clip of the "crash" that we used the smoke bombs for, but monetarily speaking, I really think the bug fogger and fog juice option is most cost effective.
Good luck, and let us know how it goes!
