You just make sure that the noise sampling microphone input is located outside the cabin of the car. Stick it in a wheel well or under the back bumper or something. That way it picks up road noise instead of music sound.
It will be picking up the ambient noise in the immediate location of the microphone, which will bear little relationship to the noise inside the cabin of the car.
The noise inside the car comes primarily from wind passing over the various external protuberances of the car, from the tires contacting the road, and to a lesser extent from mechanical sounds made by the car itself. These noises enter the cabin of the car after being "processed" by the material of the car itself, that is, the sound from the tires is conducted through the wheels, suspension, and body of the car until it resonates inside the car. A similar process occurs with the wind noise. In both cases, the "quality" of the sound (frequency, intensity, etc.) outside the car is not the same as what you hear inside the car.
If all you want is volume adjustment... well, maybe. But it would probably be easier to tap into the car's OBD system to get the verhicle speed, or, for about $10 you can buy a magnet and a sensor switch (used on bicycle computers) and do your own independent measurement of wheel speed.
I don't think noise cancelling would even be possible without losing a lot of quality along the way. If the microphone were located outside the cabin, it would not be telling the proposed box the proper sounds to cancel, and if it were located inside the cabin, it would be "hearing" sound from the stereo and cancelling that as well as cancelling the noise. Even if you fed the signal from the stereo directly into the box and told it not to cancel any of that, some of the stereo frequencies would coincide with road noise frequencies and get cancelled anyway.
Noise cancelling works with headphones, where there is no "competition" between internal and extrernal sound. I don't see it working in a shared acoustic environment.
But then, my ignorance of such matters is only exceeded by my willingness to expostulate on them, so who knows?