The name of the succulent is confusing as it's actually not a palm. There are some freezing temperatures in our area, but nothing like the extreme winters elsewhere. It is up to you when the bloom stalks should be cut. Cut back on watering in the winter when the leaves have fallen off. This will allow your succulent to have access to water for longer periods of time and make it more likely that they will survive. Many of the leaves can root and grow new plants but it takes a lot more time than stem cuttings.