Will insurance pay for weather damage on a breaker box that is on the outside of the house?

The best advice anyone can give you is to ask your insurance company about your policy to find out if it covers accidental damage on a breaker box on the outside of your house caused by bad weather. There is no general answer possible because - let alone differences which exist between the insurance industries in different countries, and differences which exist between different insurance companies in the same country - every insurance company itself probably issues many different types of policy to cover damage and other losses to buildings.