Yes, in many cases you can leave an urban planter box outside all winter, but it depends on the planter material, the plants inside, and how much freezing and wind your area gets. A container is more exposed than garden soil, so its roots can freeze faster and harder. If you prepare it well, the planter and its plants have a much better chance of surviving until spring.
First, check the planter itself. Frost-resistant materials such as thick resin, fiberglass, concrete, or treated wood usually handle winter better. Terracotta, ceramic, and thin plastic can crack or become brittle in hard freezes. Metal may rust or conduct cold. Make sure the box has drainage holes and never let water sit in a saucer, because trapped water can freeze, expand, and damage the container or drown roots.
Second, think about the plants. Cold-hardy perennials, shrubs, and small evergreens may be fine outdoors if they are rated for your winter zone. Tender annuals, tropicals, and less hardy plants should be moved indoors, into a garage, or to a sheltered spot. If you want to keep them outside, group pots together, wrap the planter with burlap or bubble wrap, and add mulch over the soil surface. Elevate the box on pot feet or bricks so it does not sit directly on freezing concrete or paving.
Watering still matters in winter. Evergreens and container plants can dry out when the soil freezes and winter winds pull moisture from the leaves. Water on mild days when the soil is not frozen, but avoid soggy soil. A layer of mulch helps stabilize soil temperature. Windbreaks made from burlap screens can also reduce damage.
If the planter is empty, clean it, let it dry completely, and store it upside down or covered in a sheltered area. If it stays outside, tilt it slightly so snow and rain cannot collect.
In short, you can leave an urban planter box outside all winter if it is durable, drains well, and contains plants suited to your climate. With insulation, drainage, and a little protection, your planter can make it through the coldest months and be ready for spring.