That's an excellent question, and one I wondered about myself before investing in some heavy-duty bins for my backyard. From personal experience and researching various models, I can tell you that performance varies dramatically depending on the material and construction quality.
For most modern, commercially-available outdoor trash cans designed for residential or public use, the short answer is: well-made ones hold up surprisingly well, but with important caveats. Plastic bins, typically made from polyethylene, can become brittle in prolonged freezing temperatures, making them prone to cracking if impacted. Conversely, in intense, direct summer heat, some plastics can soften or warp slightly, especially if they're dark-colored and absorbing sunlight. The key is UV-stabilized, high-density resin, which resists these effects far better.
Metal cans, usually galvanized steel or aluminum, excel in heat but can be problematic in cold, damp climates where rust may accelerate. Powder-coated or stainless-steel options are champions for temperature extremes, though they come at a higher cost.
The real enemies are less the temperature itself and more the combined factors of UV radiation, moisture, and physical stress. A quality can rated for all seasons will specify a temperature range (e.g., -40°F to 140°F). My advice? Don't cheap out. Look for thick, reinforced walls, robust hinges, and lids that don't become unworkably stiff in the cold. Proper drainage holes are also crucial to prevent ice damage from trapped water. With a good product, you should expect years of service through all seasons.