Undead trees are located in the front yard of Draynor Manor. Unlike the dead trees surrounding them, they attack players walking past them for small amounts of damage. They also cannot be cut down until having done so during the Animal Magnetism quest. This requires a blessed axe and a Slayer level of 18, receiving undead twigs instead of logs.
It is possible to receive a bird's nest from an undead tree. However, this nest will always be empty.
The right click of an undead tree
They can be spotted by their yellow Examine option, identifying them as a NPC instead of a tree, and are also slightly smaller in size.