The closest thing to a car I would consider would be a Suzuki Sidekick with the biggest tires you can fit on it + a good spare. Hopefully only two people on board, and small folks to boot and don't pack anymore than you can get into the little sucker.
Next best would be something like a Tacoma or so. Better would be a full size p/u w/a back seat and a camper shell of some sort.
I'm from back east and the open county and distances one can get away from services of any kind causes great anxiousness. And I've been out here for more than 40 years.
When the guys mention gumbo they mean real slick, slippery and gooey stuff that without mudders or chains you're pretty much screwed.
I don't know about your hunt areas but our corner of Idaho has plenty lava rock. If so, top notch tires are a confidence builder.