A wolf can build or find a den for winter and keep itself warm in very cold temps. But put a dog out in the freezing cold without shelter and they can get frostbite or freeze to death. Many dog breeds or short haired cat breeds were not bred to withstand freezing temps and can freeze to death if it's cold enough. Other than arctic breeds which are made for colder temps, most breeds are gonna get too cold past a certain degree.
Wild animals have adapted to weather for years, but small domestic animals have been bred for years being cared for by humans, so they look to humans to keep them safe from things.