The short answer is: maybe—and often yes, but only if the planter, soil, drainage, and plant are set up for it. Cold air alone does not usually crack a good container. The real enemy is water. When water in the soil or inside tiny cracks freezes, it expands. That pressure can bow, split, or crack a planter, especially if the soil is soggy and the container is rigid or already damaged.
Material matters most. Frost-proof resin, fiberglass, HDPE, flexible plastic, and many composite planters can stay outside through winter. Glazed ceramic, terracotta, thin plastic, and some stone or concrete planters are more likely to crack. Wood usually does not crack like ceramic, but it can warp, rot, or loosen at the joints. Metal may not crack, but it can rust, dent, or freeze plants faster because it conducts cold.
Drainage is just as important. A planter left outside must have open drainage holes, and it should not sit in a full saucer or a puddle. Raise it on pot feet, bricks, or a plant stand so water can escape. If the drainage holes freeze shut, melting snow and rain can fill the soil, then refreeze and expand. That is a common cause of cracked urban planter boxes on balconies and rooftops.
The plant also affects the decision. A hardy perennial in a large, frost-proof container may be fine. But roots in above-ground planters get much colder than roots in the ground. If your plant is only borderline hardy in your area, move it to an unheated garage, shed, or basement. If you leave it outside, choose a spot against a building, out of the wind, and cluster pots together for insulation. Snow can actually help by insulating the soil, but do not rely on it.
You can protect a planter that must stay outside. Wrap the sides with burlap, straw, bubble wrap, or blankets, but keep drainage holes open. Add a thick layer of mulch over the soil. Stop fertilizing in late summer, and reduce watering in fall. Do not keep the soil bone-dry, because roots can dry out in winter, but do not keep it soggy either. Aim for slightly moist, not waterlogged.
If the planter is empty, the safest move is to clean it, dry it, and store it upside down or under cover. If that is not possible, make sure it drains and is not collecting water. If the planter is valuable, antique, or already has hairline cracks, do not gamble. One freeze-thaw cycle can turn a small crack into a broken pot.
In short, you can leave an urban planter box outside all winter without cracking if it is frost-proof, well-drained, sheltered, and planted with something hardy. If it is ceramic, thin plastic, waterlogged, or exposed to repeated freezing and thawing, cracking is a real risk. When in doubt, move it, empty it, or protect it before the first hard freeze. That is far easier than replacing a cracked planter in spring.