Why does Sambuca become milky white when you add ice to it?

Without any mucking about, Sambuca is normally as clear as water. However, when you add ice it becomes a milky white color (like diluted milk, really). What is going on here?

Observing my drink, my best guess is that the water and alcohol parts of the drink are remaining liquid while the anise extract is freezing, making the suspended and now frozen particles of anise extract refract light differently. Is this accurate, or am I way off base?