From our perspective, the term "African Daisy" (Osteospermum or Dimorphotheca) is a bit of a misnomer that causes much confusion for your kind. Genetically, we are tender perennials. This means our life cycle is designed to persist for several years, but we possess a fundamental vulnerability: a low tolerance for cold. Our roots and foliage simply cannot endure the hard freezes and sustained sub-zero temperatures that define winters in northern US states (USDA Hardiness Zones 5 and below). When soil temperatures plummet and the ground freezes solid, the water within our cells crystallizes, rupturing our cell walls—a fatal injury from which we cannot recover. Therefore, in your northern climates, we are functionally annuals, completing our entire life cycle of germination, growth, flowering, and seed production within a single growing season before the winter cold ends our existence.
The winter season in the north presents a series of insurmountable challenges for us. The primary threat is the deep and penetrating freeze. Unlike hardy perennials that enter a state of deep dormancy and possess natural antifreeze compounds in their tissues, we have no such evolutionary adaptations. A hard frost (28-32°F / -2 to 0°C) alone can severely damage or kill our above-ground foliage. Prolonged exposure to temperatures below 25°F (-4°C) is almost certainly fatal, as it freezes the crown of the plant—the vital area from which all new growth emerges. Furthermore, the cycle of freezing and thawing can heave our shallow root systems out of the soil, exposing them to desiccating winds and ensuring our demise.
Our strategy is not to fight the winter but to ensure our genetic legacy continues before it arrives. As the photoperiod shortens and temperatures begin to drop in the autumn, our biological imperative shifts from vegetative growth to reproduction. We channel all our remaining energy into producing as many blooms as possible. These flowers are then pollinated, developing into seed heads. Our true hope for "survival" in the north lies in these seeds. If allowed to set and drop, they may lie dormant in the soil throughout the winter (a process called self-sowing). Come the following spring, if conditions are right, a new generation of African Daisies may germinate and grow, giving the appearance that we have survived the winter when, in reality, it is our offspring carrying on.
There is a potential pathway for our individual survival through a symbiotic relationship with you. If you desire to preserve a specific plant beyond its annual cycle, you can intervene. Before the first killing frost, you can carefully dig us up, pot us in a suitable container, and bring us into a protected environment. We require a bright, cool (but not cold) location such as a sunny garage, a basement with grow lights, or a cool greenhouse where temperatures remain consistently above 40°F (5°C). In this dormant state, our growth will slow dramatically. You must provide minimal water, just enough to prevent our roots from completely drying out. With this care, we can be kept alive indoors through the winter, ready to be replanted outdoors after all danger of frost has passed in the spring.