The length of fermentation, whether cold or room temperature, is always determined by what you have in your dough that will help sustain the yeast. This includes several things, the most basic of which is nutrients. Simple nutrients like sugars are obviously needed, whether added by you or converted by enzymes. You'll likely want to use a little less salt than a room temperature dough formula, because although the yeast already slow down because of the lower temperature, enzymes are even more inhibited by salt. If you're planning on a really long fermentation, use sea salt so that additional micro-nutrients are available to the yeast for cell maintenance; and if you use sugar, use one with minerals like zinc, magnesium, or phosphorous (e.g. brown sugar, maple sugar, raw cane sugar, honey). Depending on the condition of your flour, you can probably sustain a small amount of yeast (0.25% or less) for about a week at 41 F with no additional nutrients. For a three day rise, you shouldn't have to do anything but use less yeast.
How the dough is stored in your refrigerator will make a difference too. Ideally during a long, cold rise, you want the excess gas to escape, but not the moisture. During a 24 hour rise, keeping it completely sealed is fine. Storing the dough in a plastic container (as opposed to metal or glass) will spare the surface of the dough from extreme temperature gradients. If your refrigerator is really cold like mine, where the temperatures reach 32 F or below near the back, double-up your container.