Hi Mike,
Check out the Cleanup section on the Effects tab, and the Noise Reduction tools in particular. I just tried this out by mixing some brown noise (made with ToneGen) with spoken audio. I was then able to recover a good approximation of my original audio with the following process:
1. Apply Auto Spectral Subtraction. The brown noise was less audible.
2. Apply Auto Spectra Subtraction again. The brown noise is now only audible in the gaps between words, and quite soft.
2. Apply a Noise Gate with settings: Threshold -18dB, Hold 20ms, Attack 0ms, Release 0ms, Attenuate -10dB. Here the threshold is the most important setting, because it determines what gets cut out. I made the attenuation fairly small so that the words didn't sound clipped.
You asked specifically about using a snapshot to reduce the noise. To do this, select your snapshot, and use 'Grab noise sample from selected area for spectral subtraction'. Next unselect your snapshot (so that the following will apply to the whole file), and use 'Spectral subtraction based on noise sample'. You may need to do this a few times to get a better result. I tried this, but for me the Auto Spectral Subtraction worked better.
Alex