IMO, I think it depends on what type of story it is as to whether I care about the tree. Details like that can give a story verisimilitude and create an evocative picture in the reader's mind. On the other hand, if the focus is more on action or something, detailing what kind of tree it is and expanding on the setting might kill the narrative tension. It all depends. But in the right fic, I think exploring the landscape more could be very interesting.