That picture is also in the book Nicholas & Alexandra: The Family Albums. The caption reads: "August-October 1910, Friedberg, Germany. Anastasia. The little girl is wearing a woman's clothes: long coat, cane, hat and veil, most probably for a trip in the car. This type of transport was hardly ever used in Russia, for they did not often travel far from the Imperial residences, but abroad, in Germany in particular, they were often out in one of these marvellous machines."
Good question about the walking sticks, Janet! I think it was just a fashion accessory as I have seen other pictures of the girls using one and of course they didn't really need one.