Wild Free-Roaming Horses and Burros Protection Act of 2022 This bill modifies requirements under the Wild Free-Roaming Horses and Burros Act, including by directing the Department of the Interior to (1) establish regulations that require humane treatment of the animals during handling, management activities, removals, euthanasia, holding, and other activities; and (2) take actions to correct, prevent the recurrence of, and record violations of such regulations. The bill also prohibits Interior from destroying such animals unless they are fatally injured or terminally ill.