Homeowner insurance policies typically cover damage to a water heater cover if the damage is caused by a covered peril, such as a sudden and accidental event like a burst pipe or a fire. However, if the damage is due to regular wear and tear, negligence, or lack of maintenance, it may not be covered. It's essential to review your specific policy to understand the extent of coverage and any exclusions that may apply. If you are unsure, it's always a good idea to consult with your insurance agent.