Further note to Elizabeth san's explanation:
yumeoibito means "deam-follower" though I don't know if such a word exist in English...
yume wo ou = to follow/chase (one's) dream
yume wo ou hito = a person who follow his dream
yume oibito is a word made from yume (noun, dream) + ou (verb, to follow/chase) + hito (noun, person).
"Yume" indeed is "dream" but "no" is not "field", it is a particle and in this case it can be translated as "of". "Yoake" is "dawn".
Yoake no = "of dawn" but without any background/context, I cannot tell whether it modify only "yume" or the whole "yumeoibito".