The convertible I saw last weekend that slid on ice and flipped outsides own when it went off the verge probably weren't so happy about the soft top.
Besides which, in the mountains 4wd is a blessing and means you don't have to put chains on at the police blocks.
This is a real thing I too would be concerned about when going on a simple driving holiday to California with a partner.
Also OP, have you considered the fact that IED's may be placed along the roads? Probably worth renting an amoured car of some sort because once in a computer game, Battlefield 3, I saw a car get blown up.