Mushrooms will grow on a willow tree when it is dying or dead. The mycelium webs through the dead and decaying wood fibers of the willow tree consuming nutrients and water, and has enzymes that break down lignins that hold wood fibers together, turning the tree into fine humus.
Although many types of mushrooms will grow on a willow tree, the edible oyster mushrooms and the edible golden honey mushrooms seem to favor growing on it. Mushroom hunters seek out willow trees to harvest these varieties.
Willow trees can be found growing near water or in wet areas, and the high humidity in these areas also favor growth of mushrooms. During drought years, look for mushrooms near willows after a significant rainfall.