For myself, I think that "nature-based" is best understood as when the idea of nature (however "nature" is conceptualized) is understood as a central organizing principle of the religion -- to the point that if you chopped out all references to nature, you could not practice the religion in a recognizable way. That's it. No commentary on specific forms of worship, or how one conceptualizes the gods, or whatever -- there's tons of different possibilities. And moreover, I think it's more of a continuum than an absolute category.
I like this definition, but applying it takes more knowledge of the specific religions in question than many people who like to throw the nature-based label around have. Too often people assign the label without really knowing much about the actual religion they are labeling. For example, Hellenic Paganism seems to often be classed as nature-based because what people know about it is based on incomplete or very biased knowledge -- for example, the fact that a version of the Demeter/Persephone/Hades myth is central to some popular forms of Wicca or what one learned from reading Bullfinch's Mythology. Bullfinch's Mythology -- like most of the stuff to come out of that era -- is based on a 19th century English view of the Greeks. And while the Demeter/Persephone/Hades myth is indeed central to some forms of Wicca, it wasn't central to belief or worship in ancient Greece.
Whereas a Greek Recon/Hellenic Pagan devoted to Athena following the Athenian civic festival calendar would not lose too much beyond some imagery and a festival or two -- you could still recognize it. One devoted to Demeter, though, would be flailing.
A religion devoted mainly to Athena or one devoted mainly to Demeter (or any other single Hellenic deity) would almost certainly be a modern construct. The ancient Greeks had many deities -- public festivals and such clearly show this. Athena was the patron deity of Athens, but Athens still have festivals for the other major deities. Even if one was personally especially devoted to a particular God, one would not ignore the others completely lest they become angry. Having a special relationship with Hermes isn't going to help if you need healing -- you'd need to call on another deity (perhaps Apollo) and Apollo would be unlikely to help if you snubbed him because you were too devoted to Hermes.