@Enrique, IMO, it might be good to have a falling animation (perhaps only the trunk, without leafs), then it still can be decided how to use it (drop after cut down, cut down then gather, ...)
But I do wonder how a fallen tree would look on uneven ground. Trees are always supposed to stand straight (as opposed to keeping a straight angle with the ground), but when they fall, they're still the same actor, but need to align to the terrain better. Nothing too hard to code though, we just need to think about it.