So many annuals are actually perennials. They just get dug and replaced because they are not pretty enough during their off season. For warm season annuals, winter is the off season. For cool season annuals, summer is the off season. However, if left alone, many annuals that are actually perennials go dormant so that they can survive through their off season to regenerate and perform again for another season, or several seasons
Cyclamen and various primroses are cool season annuals that are in season now. Cyclamen will go dormant and defoliate as the weather gets warm in summer. Primroses do not defoliate, but get rather runty through warm weather. If planted with other light duty warm season perennials that take over for them, no one notices. For example, primroses are colorful enough now to distract from tired fleabane. By the time primroses fade, the fleabane takes over.
Chrysanthemums are among the flashiest of perennial annuals, but also have a short season. They typically get planted while blooming in autumn, but finish their bloom cycle before winter. After all the rain and cool weather . . . and then a bit of warm weather, some are already dying back to the ground; but closer examination might reveal new growth already emerging from the roots!
Nasturtiums can obscure regenerating chrysanthemums nicely. If the frost sets them back, they recovery quickly. They will bloom more colorfully by spring, and continue until summer gets too warm. By that time, the chrysanthemums should be filling out nicely to bloom by autumn. As the chrysanthemums finish, the nasturtiums will have sown their seeds, so that the process can start over again. Neither chrysanthemum nor nasturtium need to be removed while out of season. They only need to be pruned back and groomed accordingly.
Coleus, impatiens, fibrous begonias and maybe even polka dot plant that were only moderately damaged by frost might be salvageable if they can stay put long enough. That is the advantage of growing them in pots with other small perennials that will cover for them when they die back or need to be pruned back.