It is already appropriate enough to describe this phrase as an epithet, of the sort with which the Homeric verses are rich. However, we might also call it a descriptive phrase. As it applies human attributes to aspects of nature, we could also say that it is an example of pathetic fallacy.
Pathetic fallacy is a conceit in which natural elements are afforded human motivations and attributes and are described as if they are human. In this instance, dawn is described as being human in that it has rosy fingers, whereas in actuality, this is only a figure of speech. We could also interpret this as a metaphor, where the clouds spreading across the early morning sky, limned in pink and gold, are represented as the fingers of dawn.