Small-diameter Timber and Underutilized Material Act of 2022 This bill addresses the removal of small-diameter trees in fire hazard areas. Specifically, the bill prohibits the Forest Service (FS) and the Department of the Interior from charging a fee to authorize the removal of a small-diameter tree in a fire hazard area, including a fee for a special use permit; or recovering any processing or monitoring cost of authorizing such removal. The FS or Interior may charge a fee for removal of a small-diameter tree of a particular species of tree in a fire hazard area upon determining that the fee is appropriate and disclosing that determination to the public.