Cast Stone, or concrete, is a porous absorbent material. Unfortunately that makes it especially vulnerable to freeze/thaw cycles. The highest risk pieces are cast stone fountains and birdbaths because they are meant to hold large amounts of water, so when the water freezes and expands the pieces may develop cracks. Sometimes they are large noticeable cracks, but most commonly they are hairline cracks that won’t be seen but will weaken the piece and shorten its lifetime.
To avoid this from happening you must ensure that none of the pieces are holding water before the first frost comes. That means either draining water fountains and birdbaths and taking them inside for the winter, or at least draining and covering them up well. All pumps, tubing and rubber gaskets should be removed from the fountains for the winter and stored inside.
Statuary is less problematic. While it’s preferred to store it indoors, it can be left out if lifted off the ground at least an inch. That will ensure that it won’t freeze to the ground.
Planters should be either emptied and raised (to avoid water collecting at the bottom) or taken inside for the winter months. A plastic liner can be used for a large outdoor planter to simplify winter care.
Ceramic pieces need the same care as cast stone fountains and birdbaths because clay is also porous and will crack from freezing water.
Granite requires the least winter care. The main concern for a granite fountain is the fountain pump and rubber fittings, which should be disassembled and stored inside for the winter. Otherwise granite pieces don’t require being drained or covered.