> I guess the idea was that the inside of the car is cleaner than the outside air.
I'll say this isn't so.
Louise and I camp at Burning Man every year, and the playa surface is a very fine powder. Maybe finer than volcanic ash, maybe not. A sample video:
http://www.flickr.com/photos/civex/2831873456/The worst dust storm we've been in was when the visibility was four feet; when visibility is four feet, you can't see the ground you're standing on.
The interiors of every vehicle at Burning Man is covered in dust. Worse, all the air intakes are full. When you start your car/truck/whatever, you get a huge blast of powder out the A/C vents that lasts a long time, further coating all the front seats in another layer of dust.
The seals on the doors don't protect against intrusion of the powder, the filters (if any there be) on your A/C intakes don't protect. I would not expect the interior of any vehicles in a Mt. St. Helens type eruption to be any cleaner than the outside air, _especially_ if you have a window cracked open and "sealed" against air.
Last week I turned on the air conditioner on our van for the first time this season, and I got a whiff of playa powder out the vents. shrug - fortunately it's a reminder of great adventures, so it's not a problem. The van was on the playa last American Labor Day.
I would suggest you're better off changing the air filter frequently. I'm not sure how long one would expect ash-falls to continue, but clogging the air filter is likely to take some time. I'd start with some research on that answer before doing anything else. If heavy ash were a concern for me, I'd have a couple of air filters in the trunk.