Games : Skyrim: Is it possible to play with new DLC in an old world?

To be precise, what I mean is, is it possible to buy the game with no DLC, create a world (and play a fair bit), but then to buy the DLC, install it and play on the same world with the DLC? I don't think you could, but it would be good to have.

Also, I am playing on the XBox 360.