Good question! We are in zone 7b and the anemone I planted (anemone coronaria) are adapted to zone 7-9 so this is an ideal climate for them.

In areas that are colder, you can dig up the corms and save them to plant out again in spring.

How well your anemone naturalizes will depend on the variety and where they are planted. The herbaceous perennial ones (anemone japonica) are the best bet for establishing in gardens, but these flower in fall rather than spring.

Here's a really helpful guide to different anemone varieties and their preferred environments: https://www.longfield-gardens.com/article/All-About-Anemones.