Rock Pigeons do not fly south for the winter, according to All About Birds. In fact, once a nesting place is chosen, pigeons stay year-round. There is no migration during summer or winter months.
Pigeons are perhaps one of the most useful birds in history. They often carried messages during World Wars I and II, where they were an easily unnoticeable and small target for enemies. The reason pigeons are so invaluable is their ability to find their way home from practically any location. It is thought that in addition to sight and sound, pigeons use the earth's magnetic fields and the orientation of the sun to find their way.