I would like to give some prespective to this entire tan issue.
My grandmother was born in 1888 to a well off family, with a small household staff. To this day, I can remember my grandmother, as white as marble to her last day, telling me in the early 1970's that being tanned or sunburned was undesireable and showed that one had to work out of doors and was of the lower classes. My mother followed this rule and wore gloves and a large hat when tending her flower gardens. To this day my eldest sister wears white cotton gloves while driving her car to avoid sun damage to her skin.
Does this give everyone an idea of how unusual and peculiar getting a tan was for Russian Grand Duchesses. I would think that it was Alexandra who introduced this notion of sunbathing to her daughters as she was such an anglophile. The new concept of sunbathing as a symbol of status came from the returning officials of the British Empire who were easily noticed in London and elsewhere with their well tanned faces. The tan meant that the person was well travelled, had experienced exotic lands and cultures, etc., etc., etc.
David