If you can figure-out how to wire-in a manual switch, you can replace that switch with a relay and control the relay with the Arduino. (Then, you can replace that switch with a "3-way" (center off) switch running into the Arduino. The switch can then select "up", "down" or "automatic".)
The logic is fairly simple. Have you done any programming before?
My questions are is this possible and how would I calculate for the board the speed of the car?????
That seems like the hard part. Every car is different. You'll have to figure-out how to tap into the car's speed sensor or speedometer. If the car has an analog speedometer, sometimes they are electrical and there is a DC voltage that's proportional to speed. You'd have to find the right wires and hook-up a multimeter to measure the voltage at 50MPH. The Arduino has an analog-to-digital converter that goes up to 5V. Since the electrical system is 12V, you'd probably need a voltage divider. (Even if you are getting less than 5V at 50MPH, you need to protect the Arduno from higher voltages.
If you can't do that, you might be able to add a sensor (optical or magnetic/hall effect) to your drive shaft or wheel to count the RPMs. Or, you could use a pitot tube to measure air speed.
My car has a rear spoiler that activates at 94mph and then fully retracts about 45mph...
...to control it raising and lowering round about 50mph.
You'll want to keep some of that concept of lowering it at a speed below the activation speed. Otherwise the wing will "chatter" or continuously move up & down when you drive around 50.
P.S.
If you can't find any useful information about your car's electrical system in a car forum, you might try talking to a "hot rod" or "racing" mechanic... Not your "factory authorized mechanic"... Someone who knows your car but is not afraid of making unauthorized modifications. 
**P.P.S.**Or if you can't get the speed sensor figured-out, how about this option? A manual up-down switch, plus it automatically goes down when you shut the car off? Something like that could easily be done with the Arduino (after you figure-out the up-down relay wiring), or it's simple enough that it could be done with logic circuits (no microcontroller or programming). You could probably even do it with just relays.