With hurricanes, freight movements are usually affected in three stages:
Before the storm, if it is predicted in advance, shippers and FEMA rush to move freight in and out of the area where the storm is expected to make landfall, and truckload rates rise sharply.
During the storm, nothing moves in or out of the affected area. It's just not safe. FEMA and other organizations will move emergency relief supplies to locations just outside the storm zone, so they're ready to act as soon as roads are clear.
After the storm is over, emergency supplies are brought in, and inbound rates shoot way up, at least for a while. Van and reefer freight move in first, followed by flatbeds hauling construction equipment and materials.