If your website is hosted inside a datacenter that is located in a storm’s path. There is a high probability that there may be a outage if a storm or hurricane were to pass through the area. Depending on where your datacenter’s location is, there can be at different times of the year, where you notice more outages than usual.
Your datacenter has your covered
When your web host decides to use a datacenter or build their datacenter in a region where there is a known history of storms. Your web host will probably have contingent plans in place when there is a storm. The contingent plans will include having extra diesel on site to power backup generators if the main power feed goes off for any reason. Your web host will probably have extra food and water also at the datacenter during a storm. The number of employees working at the datacenter during a storm will vary but it maybe a skeleton crew (not many, just the necessary people).
Fiber cuts are your worst enemy
The only major issue during a hurricane, tornado, or any other storm is the fiber connections. If the datacenter loses power they will have backup generators to continue powering the servers. If the fiber connection is damaged for any reason. It may take a while to repair. Depending on how many different IP transit carriers your datacenter uses. If one IP transit path is damaged during the storm. The other IP transit carriers will have to pickup the remaining bandwidth. If the remaining IP transit carrier’s fiber connection to the datacenter is not large enough then your datacenter will have some issues sending and receiving data.