Plain frozen cream is hard as a rock. Sugar makes it softer, but also lowers its freezing point (the dissolved sugar molecules get in the way as the water molecules settle into ordered crystals). So sweetened cream freezes well below the freezing point of pure water, and can’t freeze in the slush that forms when a warm object is placed in snow or ice. What made ice cream possible was a sprinkling of chemical ingenuity. If salts are added to the ice, the salts dissolve in the slush, lower its freezing point, and allow it to get cold enough to freeze the sugared cream.