The name of this succulent is confusing, as it's not a palm at all. It does get cold here, but not in the same way as areas with very severe winters. It is upto you to decide when to cut the bloom stalks. Cut back on watering in the winter when the leaves have fallen off. Your succulent will have more water and can survive longer without needing to be watered as it has greater access to water. While many leaves are able to root and produce new plants, the process takes much longer than that of stem cuttings.