If a hurricane warning is issued by the National Hurricane Center for the Orlando area—or for your place of residence—within 7 days of your scheduled arrival date, you may call in advance to reschedule or cancel your Walt Disney Travel Company Disney Resort Hotel Package and most room only reservations (booked directly with Disney) without any cancellation or change fees imposed by Disney.
If you have products and services provided by third-party suppliers included in your vacation—such as airlines, hotels, car rental agencies or travel insurance companies—you will continue to be responsible for any non-refundable payments, as well as cancellation or change fees assessed by those suppliers. The policy does not apply to certain special events or dining experiences.
In addition to the official policy, you might take a look at this podcast from last year that discusses the experience of staying in Central Florida during a hurricane:
Source: Walt Disney World