Refrigerating any type of buttercream is mainly a question of the climate in your kitchen. If you are able to keep this on a cool counter, in an airtight container, this will keep well at room temperature for about 4 days easily. If your kitchen is particularly warm or you are having a heatwave, you may find it best to refrigerate so that the frosting doesn't melt or become runny. Buttercream will taste best at room temperature, so if you are serving after refrigeration, allow this to set out for about 20 minutes to start coming to room temperature first.