Vladimir Horowitz was a notoriously private person. He didn't trust most people in his life, was always suspicious of friends, and weary of the press. He WAS a very shrewd businessman, but that's for another post.
This being said, there are precious few recorded 'interviews' of Horowitz in an unguarded, relaxed state. For some reason, Horowitz took a liking to Mike Wallace and would let him into his home with cameras, microphones, and the like, and would interact with him in such a way that you'd never realize Horowitz had such an aversion to the media. A little more on this can be found in this very interesting book.
Here's a great little excerpt from a 1977 interview in Horowitz's home. He's relaxed, enjoying himself, and joking around at the piano. It's a real treat to see even just this little bit into his personality.