Harvesting and storing edible roots for winter use is a custom that has been practiced for many years. Root storage can be done using several methods, depending on where you live and how cold your winters are.
In the Ground
Some roots, like Jerusalem artichokes, evening primrose, and burdock can be stored by simply leaving them in the ground and digging them up when needed. The disadvantage with this method is that when you're ready to use them the ground may be frozen, weather may not be cooperating, or you may not want to take the time to go out and dig them. Another problem in areas with warmer temperatures is that underground rodents and beetle larvae may feed on them before you get to them. Or if there is a really warm spell, some roots, like Jerusalem artichokes, will start to sprout.
Cold storage involves keeping roots alive, but dormant. In areas with cold winters where the ground remains frozen for periods of time, having roots in storage is convenient. When you dig them up, be sure to keep some soil around them. You want to keep them cool enough so they don't grow but warm enough so they don't freeze. If they dry out, they will die also. A root cellar or basement can be used for some roots. If you have an outbuilding or other storage facility with good ventilation, it can be turned into a drying room as well. A wooden or cardboard box can be used for small quantities or they can be layered in mounds or pits between sand or straw. Old newspapers can also be used for layering. You may want to try several methods in the beginning to see what's going to work best for you and the area where you live.