First, Sorry to everyone who thinks I'm annoying for being almost every other post...I'm just the kind of person who likes to respond....I hope it's not against the rules or something...
Secondary, Yggdrasil represents the beginning and end of all things. It is the tree of life, and if it dies, so does everything else. the Serpent represents the ever-present possibility/inevitability of the end of all things. But, if Yggdrasil dies, it dies, and from it's body, a new tree would rise. And though it is chewing on Yggdrasil, essentially destroying it, it also provides life in its own way. That presence, pushes Yggdrasil to keep going, if the serpent dies, so does Yggdrasil, and then a new one would rise.[I don't know much about Norse mythology, but it does derive from certain aspects of Archaic mythology, which I do know about, so bear with me on my thought processes]
Again, it does come down to what me and Magma were talking about, Creation, Destruction, and Chaos. The deer, represent life, nature. Where they walk, trees, flowers, plants grow. [The Spirit of the Forest comes from the same myth]. The Eagle, whom can peer into the souls of living thing, represents Judgement. In various versions of the myth, it also represents Death, or destiny, in that it can decide when someone is to die. And the serpent, represents Chaos, that which is in all things. As Yggdrasil represents all things, and the serpent, not just chewing at its roots, is part of Yggdrasil. They need each other. [And a Draconequus, with the body of a serpent, would again fit well here. If you look at different ancient arts of different serpent Deities, they are somewhat...squarely drawn, usually in the shape of an S or similar, so the artwork of this Legendary could be drawn in much the same way to look like a Z]
There are other ways of portraying it, Heart, Body, and Mind, etc. But different mythology, I'm done with this spiel.