Do all birds fly south for the winter?

No. Some birds do not migrate at all, but live in the same range all year long. This is especially true in warmer climates, but some birds even stay in the Arctic all year. Some birds that migrate move in other directions, such as east or west, or from higher elevations to lower elevations, to get to where they can find food or shelter in the winter. And or course, in the Southern Hemisphere, most birds fly north in the winter.