Consider what this expression does to dawn. What is the expression "rosy fingered dawn" giving to dawn? Hopefully you should be thinking that it is giving it human characteristics, by referring to the "fingers" of dawn. Thus we can say that this figure of speech is an example of personification. Of course, in the Greek world vision, Dawn in a sense was personfied anyway as a Goddess who brought morning into being, so perhaps this helps us to understand the way that dawn is personfied throughout this great epic classic.
However, just to remind you, personification is a figure of speech where an inanimate object is given human characteristics, in either actions or appearance. Note how the "rosy fingers" perhaps refer to the effect on the sky as the sun rises and how beautiful patterns appear.