The answer depends on what type of bird. Some birds, like perching birds, have it a bit easier than seabirds and shorebirds because their little toes reflexively cling tightly to a branch or limb. But many, many birds lose their lives in hurricanes and super storms.
In the case of Piping Plovers, for the most part, business continues as usual during average inclement weather. You won’t see them sit in a tree or dune shrub because they will lose their primary advantage against predators, that of the safety afforded them by the camouflage of their sandy beach coloring.
Perhaps they’ll find a rock on the beach, or ridge in the sand, to crouch behind and out of the path of the wind. Piping Plovers are much harder to find in inclement weather because their feathers mirror shades of rain and snow and fog. Drenching rain, spring snow squalls, and biting summer sand storms won’t stop these indefatigable creatures, we see them foraging during every kind of weather event.