If your air conditioner was damaged by any of the events above (or anything else listed in your policy), you should be covered. However, homeowners insurance will not cover repairs if your air conditioner needs to be replaced due to age, neglect, or normal wear and tear.
Home warranty plans can help cover the costs of repairs to appliances, and typically cover items like home appliances, plumbing, furnaces, and air conditioning. These plans are separate from a standard homeowners policy.