For AHS registration purposes, the term "dormant" refers to daylilies that lose their foliage completely before or shortly after frost and over-winter with pointed foliage buds, usually just beneath the soil surface. Dormants will resume growth in spring.
However, in plant science, the widely accepted definition of dormancy is a temporary suspension of visible growth of any plant structure containing a meristem*. Thus technically the term “dormant” is not restricted to deciduous plants but applies also to evergreen plants, which can retain their foliage while having dormant buds. All daylilies, regardless of foliage habit, are capable of cold temperature dormancy in the technical sense where it gets cold enough to suspend growth.
* Reference: Lang et al, “Endo-, Para-, and Ecodormancy: Physiological Terminology and Classification for Dormancy Research”, HortScience, Vol 22(3), June 1987.
Also see: Deciduous.