How to make a 12V DC variable voltage supply with more than 30A output?
In short no (without linear VR type losses or with only passive type loads).

What you describe with an inductor in the output filter is a buck converter. Without an inductor, you'll only be able to chop the power up which is useful for circuits that don't mind the chopped power (think LEDs). Microcontrollers don't like that kind of power though.

If you don't want to use an inductor in a buck converter you'll be burning as much power as a linear VR.

Why avoid a buck converter when it's ideal for what you want. Also, if you decide to try and make a chopper circuit work, ensure you're using feedback back to the arduino to regulate the output voltage. What you've just described though is an inductorless buck converter, so I don't follow why you don't just add the inductor to make it a buck converter?