Go through the Dwarven Halls instead. Go far, go fast, and don't slow down for any monster!
(I realize this doesn't answer your question, but whenever I try walking through the Animated Forest, I end up fighting some trees. Either some fraction of them are hostile, or I'm clumsy; could be either. And once you start fighting trees, you can't stop, because fighting the hostile trees angers the non-hostile trees - and it's hard to tell which ones are hostile, from the up-to-eight trees surrounding you. Plus, trees spawn with time, so the level will eventually end up either impassable or violently logged.)