Powertrain: Dumb luck will be the ruling factor
It's all going to depend on the luck of the draw and how the hit occurs and how EMP waves bend around local terrain and the metalwork of the particular car.
First, remember the powertrain is already substantially inside a Faraday cage. The hood is metal, the unibody is metal and so is the engine - this largely wraps the engine package.
Nonsense to dismiss: that some cars are "mechanical" and will Just Keep Working. Nosirree. Every modern car is FADEC. Even the diesels, remember when VW cheated the Smog tests by detecting when the car was on a test stand and detuning the engine during those times? The only way to do that is with FADEC. All the other builders who were not cheating also required FADEC. So all modern cars are computer controlled.
I.E. the computer decides when (i.e. which microseconds) the fuel injector fires, and it does this in real-time on the fly. If the computer gets borked, the car doesn't stay at the last throttle position, it simply forgets to inject fuel starting right now, so the engine dies instantly.
The days of there being a basically mechanical carb/FI system with computers "only doing trim optimization" started in the 1970s with carburetors, and ended in the early 1990s -- killed off dead in 1996 when OBDII became law. OBDII requires FADEC.
But even in 1991 you'd be hard pressed to find a non-FADEC engine, probably in a light truck. Why? It's a darn good technology that makes engines run better, much longer, and more powerful too, by enabling other performance tech.
Older automobiles are practically extinct on the road
The current mix of automobiles found on the highway contain essentially zero pre-FADEC era cars. You might find older trucks without FADEC, the bigger the more likely, but only up to a certain size.
California has achieved a practical peace with classic car lovers, based on the following fact: There aren't enough of them left to make a difference. No, I mean there are loads. But they're not daily drivers. They run so rarely that they don't have a significant impact. Simply put, they're not worth regulating.
As an author, that means if you prioritize a search for an EMP-proof car, look for well-cared-for but rarely-driven collector cars. You won't find one in an office parking lot, though. It'll be in an enthusiast's garage. Or out back up on blocks, but that one won't run.
Creature comforts: All bets are off
Powertrain computers on modern cars are already extremely hardened - not against EMP but just against failing generally. Some fool shorting an oxygen sensor to 12V, a wiring harness meltdown in transmission control wiring, whatever. That's powertrain.
Now modern cars have a whole second *tranche of computers in the carbody, and those don't run the powertrain, they run the human/creature comforts. For instance the left door has 1 power window motor and Four power window switches. 14 wires? Not anymore, now it's 2 power/ground wires, and two thin little signal wires, and embedded computers in every door that chat over the signal wires.
And in recent years, as you well know, this "body-side" stuff has exploded to be the reason you buy a car - built in Nav, Siri, Alexa, smartphone integration, your music, Sirius Radio, all the smart-car stuff potentially including the autopilots - some cars more than 50% of the cost of the car is in this consumer-appeal electronic cruft.
This stuff is all body-side, and there are places where the body is not steel, but the dash and door panel interiors are not steel at all. EMP will ignore all that and reflect in unpredictable ways off the parts of the car which are metal, exposing the body-side stuff to a lot of potential damage.
So there's a pretty good chance that your engine will work but your speedo will not. Sirius works but ONStar does not, turn signals fail, and you can't roll down your windows. And the A/C won't turn on because the sophisticated comfort control took a hit, that doesn't doom you, but the fan won't run either, and that dooms you.
Ever drive a car with no fan and no windows in the summer? You cook. It's the same exact physics as dogs and babies dying from being abandoned in the car, except you happen to be moving.
However if the blower works, and a smart person could "jumper it so it's hard on" depsite blown electronics, that makes the car interior livable - though if it's a sunny day over 60F, you will need quite a bit of hydration, solar load beats you up bad. Actually for best freeway fuel economy you want windows up, A/C off, blower on max. "Windows down" is bad due to aero-drag, and A/C on takes a lot of fuel.