If you read The Catcher in The Rye by Salinger you may remember the question that one of the characters asks himself:
"I live in New York, and I was thinking about the lagoon in Central Park, down near Central Park South. … I was wondering where the ducks went when the lagoon got all icy and frozen over. I wondered if some guy came in a truck and took them away to a zoo or something. Or if they just flew away."
Since this is a famous book, the administration of Central Park felt compelled to offer an explanation here. I can confirm from my visits in IOR park from Titan that the ducks on the lake don't migrate in the winter, they are always there.
But other birds do migrate, so the question is legitimate in their case: where do they go when they go? Luckily, the modern technology is helping again, so by attaching a transmitter to a small eagle's leg a team managed to track the exact migration pattern of the bird for a couple of years. You can see in these maps how the eagle (called Narcis) flew each autumn over 10.000 kilometers from Sibiu county in Romania to Turkey, Egypt and all the way down to South Africa. And back in the spring. Isn't that amazing?