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I was thinking a single vertical stabilizer in the center just to enhance the airplane look. You could even go all the way and add some little stubby horizontal stabilizers and arrange an extra-large third taillight to look like a jet nozzle.
A vertical stabilizer might help keep Cd from increasing at high yaw angles. It also may slightly increase Cd at low yaw angles. I doubt it matters much in either case.
I wouldn't expect side-winds to affect the car much from a handling standpoint either. Look at the side cross-sectional area of an SUV, does you expect it to be unsafe in side-winds? (Sure it's going to sway more than a sedan.) Side-winds do make fabrication and attachment of the stabilizer a little more challenging, but no more so than on a real airplane.
To me its just a question of aesthetics. Is it, in fact, more fun to make a teardrop car look more like an airplane?
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