There are several options available, and I use several of them to winterize my potted fig trees.
I live in hardiness zone 6b, New York. If you don’t know your hardiness zone, you should go to the USDA website and their search form using your own zip code. People living in hardiness zone 8 and above are lucky because they don’t need to winterize their trees, whether they are potted or planted.
In general, winterizing potted figs is much, much easier than any other method. Period.
Option #1: Burying the potted tree. I am using this method regularly.
Italian immigrants winterized their planted fig trees in this manner. Feel free to search the web for more information. Warning: burying trees is a lot of heavy work. 
So, I modify the Italian immigrant method to fit my needs when winterizing my potted fig trees. I use one of my raised beds, and I first add several 2×2″ pieces of lumber at the bottom of the bed. This way, the pots will be raised a bit off of the bottom of the raised bed because I am worried about water accumulating at the bottom of the raised bed. Remember, I live in New York, and during the winter we get a lot of snow. 
I take the potted fig trees and set them on the 2x2s, and then add lots of dirt and surround the pots with it. You see, I have access to a lot of “free” dirt from my compost bins.
In the above picture you can see two Violette de Bordeaux figs that did not want to drop their leaves, and I had to wait an extra week or so for that to happen.
After the fig trees have entered dormancy, I cover them with two layers of burlap and then cover the burlap with tarp. The tarp extends beyond the interior of the bed.
Option #2: Storing the fig trees in the cellar or an unheated basement. I am using this method regularly.
Storing figs in a cellar or basement is easy and very effective. There are several stipulations to consider, though.
#1 – Mice. Make sure that mice will not be munching on the bark of the trees. A few mice would devastate the trees. A few strategically placed mouse traps will alleviate the problem.
#2 – Humidity. Sometimes cellars or basements are too wet, and this can cause a problem. A dehumidifier will alleviate this problem. I have a dehumidifier that runs 24/7/365, keeping the cellar nice and dry.
#3 – Access during winter. Perhaps the cellar is only accessible from the outside, and during the winter snow may cause accessibility issues.
#4 – Watering. You will need to water each potted fig once a month with about 3/4 cup of water. Make sure this can be done during the winter with snow, ice, etc.
Option #3 – Keeping the potted fig trees outside against an exterior house wall. I am using this method.