I did get a chance to read that passage from "No Time to Gieve" that Antonio recommended. It is quite interesting and gives a clearer picture of one of these elaborate events. After being announced to the gathering of guests, dignitaries, etc., Nicholas was introduced and entered with Olga and Tatiana. He had the first dance with Olga, and, evidently, there was an awkward period when no one asked the girls to dance. I guess it might be a bit intimidating to be the first to ask the tsar's daughter for a dance.
According to the author, this e vening continued well into the morning, and the Grand Duchesses danced quite a bit.
I know Lanie mentioned a painting, bu there must be some photos somewhere!!