How specifically did the greek idealize nature?

Almost all, if not all, of the Greek poets you can name. Probably a few poets we don't know the names of as well. Hope this answers your question. :)

δρυμός (drimos).

In some myths, man was a combination of the evil flesh of titans and the good heart of Dyonyousous

Its φύση (fisi).

Demeter (mother of Persephone who spend half the year in Hades with her husband, giving us the seasons)