Control 12V MOSFET with 5V, with PMW pass-through?
what I have read on the subject tells me that controlling a 12V MOSFET with a 5V gate leads to... Bad things. That is my first question -- what will happen if I flat out try to do this?


The drain-source voltage rating of a MOSFET doesn't give you any clue about what gate-source voltage it requires. A logic-level MOSFET will work even with 3.3V drive, for instance, and may be drain-source rated for 20V or more.


  How can I create a circuit that will allow my Arduino to control the 12V MOSFET using a 5V, 4-to-40 milliamp current, while still having the MOSFET reacting quickly enough to allow for PWM to reach the motors? 


Indeed, the bigger problem you'll face is the limited current a microcontroller GPIO can sink or source - this current is what charges and discharges the MOSFET gate capacitance and controls how fast the device turns on or off.

What you'll need to use is a MOSFET driver - this is a circuit which will take the low current drive signal from the Arduino and stiffen it sufficiently to drive the MOSFET. There are literally hundreds of monolithic driver ICs on the market from a multitude of suppliers, which work very well and are quite cost-effective.