It usually needs to be below freezing for several hours to do any damage. The water line to the ice maker is tiny, though, and might freeze more quickly. Running the fridge can only help. When we have the occasional overnight freeze here in northern Florida, and I think it may last long enough to be a threat, I put a piece of cardboard behind the external fridge grill so it isn't directly exposed to freezing air.
If it is cold for long enough (several hours), be concerned about your dump valves as well. They are also susceptible.
Former owner of 2004 American Tradition and several other RVs
Home is in the Ocala Nat'l Forest near Ocala, FL