Yes, daylilies that are evergreen in Florida can be dormant in a cold winter location. A daylily can be dormant because of the growing conditions (the environment). So a daylily that has the ability to go dormant in cold weather does not go dormant where the winters are mild or the weather is not appropriate to go dormant. That daylily can continue growing and if bred in that location would be labelled as evergreen.
Most evergreen daylilies have the ability to go dormant in the appropriate conditions (I write most since there has been no test of this ability - other than people growing registered evergreens in the north and seeing them go dormant).
