Using ohms law and the power formula I came up with (I guessed the 3volts):
1 watt LED = 3v, 9ohms and 333mA
Ohms Law doesn't com into it until you start calculating series resistors. P = V * I, so if a 3W LED has a voltage drop of 3V, it must be consuming 1A. There is some data on 3W LEDs at http://www.rapidonline.com/electronic-components/3w-power-led-74700/
The power source would be a 12v from the car battery and the Arduino needs a power supply of ? and outputs of the pins is ?.
The Arduino can run from the 12V supply, provided you are not drawing much current from the Arduino's 5V supply. The Arduino's outputs are 5V, maximum 40mA.
I would need to run all the bulbs in parallel since voltage is common in parallel
I'm not sure what you mean here. Do you need to control all the LEDs independently? If you don't, then it would be better to connect about 3 LEDs in series so as to reach a little less than the 12V you have available.
and I would need to use the voltage divider rule to get from 12v to 3v?
No, voltage dividers are only sensible with light loads. You can use a series resistor to drop unwanted voltage when feeding a LED, but dropping 12V to feed 3V @ 1A to a LED would be very inefficient, because the resistor would dissipate 9W. That's a lot of hear to get rid of. High power LEDs are best fed fro a constant current supply (especially as the nominal 12V car battery voltage varies a lit, depending on whether it is on charge or not). However, dropping 12V to 3V in this way will still waste about 9W of power.
The best way to drive high power LEDs from an Arduino is to use a switching current regulator IC such as http://www.ti.com/lit/ds/symlink/lm3404hv.pdf
for each LED. You can feed the DIM or CTRL input from the Arduino to turn the LED on/off or to dim it using PWM.