The colder the freezer, the more effectively it stops thermal degradation and chemical breakdown of the emulsion. Generally, there's a factor involved, so that increasing temperature by 2 C (or so -- might be 2x that or 1/2 that) doubles the rate of deterioration. There's a break-even point for any material, however, below which you gain nothing because cosmic rays and background radiation will fog the material even though thermal and chemical processes are essentially halted.
It would require testing your particular paper to be sure where the break point is, but it's been my understanding that -18 C, aka 0 F, is low enough for practically all photographic materials that fogging is the limiting factor. And a good top-opening chest freezer, with good seals, installed in a relatively cool area like a basement, really uses surprisingly little power (especially if it has enough mass inside to prevent excessive temperature fluctuations when the lid is opened -- plastic jugs of plain water make nice ballast for this).
