I always tell my clients to buy insurance for both weather issues (snow/hurricanes) as well as children's illness. It will cover you for both your flights and your package. Normally, if you have a delay arriving to Disney, you would call them to let them know that you are having an issue, but you will be there a day later. They will make sure that your whole stay is not cancelled. You would then make a claim with the insurance company for the missed day.