"Then the thought of Yavanna will awake also and it will summon spirits from afar, and they will go among the kelvar and olvar (plants and animals), and some will dwell therein, and be held in reverence, and their just anger shall be feared. For a time: while the Firstborn are in their power, and while the Secondborn are young."
This is about the ents, mostly, but it could also refer to Bombadil... why else mention the animals as well as the plants? Tolkien left Bombadil as a deliberate mystery, you know; like the Balrog's wings, we can discuss it forever without coming up with an answer. But this passage certainly could apply to Old Man Willow, too.