Given that water roots will not survive when planted in soil (they will be replaced by roots formed in the soil) I would start with a soil mix. Keep the pots (plants) in a well lighted window or under lights. let the vine go till late March take additional cuttings to increse the number of plants you will have or be able to share with friends.

Thanks, georgez5il, for the good advice! I will try it and report in the spring.............

There is really no need to overwinter potato slips. This is the way 'old-timers' did it. In fact, my husband's brother-in-law still does his this way unto the present time. Simply place a couple of sweet potatoes in a jar of water (set in a sunny window) up to near the top of the tuber. When the vines have grown to about 4-6 inches long, break them off right at the tuber and plant them deep in the furrow provided for them. Water in well. Starting the slips in this manner gives a very smooth slick potato at harvest time. It was the preferred method for this reason.