[susan53]

As I have said above, as a British English speaker I would always say Do you like skiing? in this situation. But I know that in US English (which is rapidly influencing UK English too) the to + infinitivestructure is also used, so I imagine it would be fine - which is why it's included in my example. Look at B's reply : Yes, I quite like to ski . Obviously, if it can be used in an answer it could also be used in the original question.
But notice that the concept of enjoyment has already been established by the co-text : My favorite sport is skiing. What about you? This is the important thing that allows the listener to understand what s/he is being asked about.