Near the beginning of Read It And Weep, we see an X-Ray of Rainbow Dash's broken wing, which shows bones extending out into the feathers. This would explain both her inability to remove her trapped feather here (as it's one of the primary flight feathers), and the apparent prehinsility displayed by pegasus wings (that is, the ability to move the feathers independently to grasp and manipulate objects; we see them lifting weights and doing pushups in Hurricane Fluttershy, for example).