Some Arduino boards are faster than others; I have never used them but there are ARM 32 bit Arduinos with serious processing power like this: https://www.sparkfun.com/products/11589

I don't know if solenoids would have the power to shift the wing while the car is in motion - I recall hearing that F1 car wings generated enough down-force to allow the cars to drive upside down, so a touring car wing must generate hundreds of Kg of down-force.