Was the princess long-since headless, and had a copy of the statues head made of ice? The cold room, and dark enough to hardly see would help hide that fact, and then eventually the head would melt on its own. The neck was bound with bandages, which could help hold the fake head on, although I guess if we're to trust the visuals given it did look like a real face. We don't see enough to constitute her moving, so it can be something else making the speech while the corpse sits there.