I guess the subject says it all. According to the datasheet, the mega328 can run off of voltages from 1.8 - 5.5V. I know that Vin goes to the voltage regulator but the 5V pin I believe goes straight to the mega328 so can I just put 3.3v on that pin and run the whole nano at 3.3v?
I've run a 328P at 16 mhz (with a crystal, not a resonator) at 3 volts (two AA cells in series). Worked just fine.
Why not just try it? Keep testing lower and lower voltages until the board stops working. Then you will know what you can and cannot do.