How large are the wool scraps? I was going to get rid of some batting scraps and then realized I could cut them down into 6.5" squares for a rag quilt cut with the Accuquilt rag quilt die. Wool batting would work well for this purpose.
It's true that fabric scraps (and even cotton batting scraps) are not good for birds. They retain moisture too long compared to twigs and grasses, which means that baby birds develop pneumonia.
I don't save really small scraps of batting and fabric anymore. Some people do collect them and, when they have enough, use them to stuff small pet beds. Some animal shelters will take that type of pet bed (call first, though, as shelters vary in what they want).