Voltage control with PWM-signal

msensor:
I had thought that although the PWM signal is always switching between high and low, that due to the rapid nature of the switching, one could assume that a voltage ranging from 0 to 5V (for the Arduino) was being emitted from the PWM output and that this could be utilized to control the gate of a MOSFET.

Assumptions always are quite some risk to take.
Do you know how rapid the Arduino PWM is switching ?
You'll be surprised by the actual number.

Your multimeter is a poor instrument to use to measure PWM signals, if you do not absolutely understand how this PWM (and the multimeter) works.
That multimeter has a slow update rate, in which it will show you an average of the voltage measured.
So what you see is something different from what's actually going on.

Robin2's description of PWM is very accurate and short.