Where Do Birds Go When It Rains?

Birds are very sensitive to the slightest changes in barometric pressure and temperature. This early warning allows them to look around and consider their options when a storm is approaching.
Some simply leave an area and avoid the worst of a rainstorm. Those that don't evacuate find somewhere secure to ride it out like a sturdy inside branch of a tree.
They have automatically clenching tendons on their toes that hold them firmly in place. They may wobble in a high wind, but they won't let go of the branch.
Each toe is connected to a cord inside the leg. When the leg is bent, the cords stretch tight and pull the toes around the branch. It takes more energy to leave the perch than to stay there.
This toe clenching also protects them while they're asleep from an embarrassing tumble out of a tree.
Robins and other ground feeding songbirds tend to burrow inside of thick hedges or brush piles to wait out a storm. They often sit in groups, especially when there are fledglings in the family.
Storms like Hurricane Sandy just two years ago, left hundreds of thousands of birds dead or orphaned. Since most Atlantic hurricanes happen in August-November, they coincide with bird migration and severely disrupt this process. Birds are blown off course and forced to land where there's no food or they're too battered to survive once they reach a safe place.
Some birds have no choice but to stay and ride out the storms as best they can. There's a federally protected breeding area located on a beach near me that was severely damaged by the last big storm and many endangered and threatened birds were lost along with their habitat.
If you want to help out the birds in your yard you can put up roosting boxes, bird houses or just build a simple brush pile for them.