"Man and the Natural World" is arguably the central theme of the book. The heath functions as its own character in addition to being an evocative backdrop that has some sort of psychic link to the characters. The characters and the heath have an interesting relationship in which people and the heath reflect each other's moods. So, yes, the heath is doing a whole lot at once – it reflects the characters, and yet also has features, feelings, even dialogue (such as with the "wind" that seems to speak).
However, this is a book about how man exists within nature and not just alongside of it – certainly not just some chummy pals. In fact, man doesn't live side-by-side with nature as equals at all; the heath is not the friendly or romantic place that the highly-romantic language might imply. Instead, Hardy depicts people as small and even overwhelmed by nature. Nature is downright Darwinian – everything boils down to survival, competition, and evolution. Of course, this is rather fitting given the impact Darwin and his ideas had on nineteenth-century thinkers and people like Hardy. Yup, the heath controls the people, not the other way around.
The heath is a largely negative force in the novel and it dooms the characters that live upon it to lives of misery or death.
Though Eustacia hates the heath, she has the strongest connection to it, more so than any other character.