Here's how I look at it. I don't think that we do ourselves any favors by regarding music as the only TRUE ART and that the claim of other endeavors to be regarded as art forms can only rest on connections to music. Sculpture is an art. But we do not say that the reason it can be called an art is because the scuptor had the radio on while he was working.
To me, figure skating is a visual art. The heart of visual art is that it pleases the eye, even as music's cliam to artistic status is that it charms the ear. I do not disparage a great composer on the grounds that he doesn't look good while he is composing. So with figure skating. Graceful gliding and well-executed blade work have aesthetic appeal to me, and this would be so whether music is playing or not. Artfully traced school figures were pleasing to the eye -- the more so when you considered their history from the days when young swains would try to carve their girlfriend's initials on the ice at the local pond.
To me, figure skating stands on its own merit. No, figure skating is not sculpture (thrugh ice carving might be

) It is quite true that if I want to admire a great work of architecture I don't go to the local skating rink to do so. To jump from this observation to "therefore skating is not an art" -- that seems like a gap in logic, not just "what me and my friends like."