I agree, white is an extremely difficult color fabric to maintain, but I think the costume designer was correct in placing the girls primarily in white. Here are just a few quotes from the ladies' fashion journals of the time period:

October, 1801, Lady's Monthly Museum
--"White dresses are the most prevalent."

December, 1805, Ireland's Mirror
--"Notwithstanding the cold and rain, a great deal of white is still worn."

April, 1806, La Belle Assemblee
--"White satin dresses will continue fashionable the whole of the spring season [...]"

June, 1806, La Belle Assemblee
--A white costume is without exception the most becoming garb for women of all complexions; but the colours which relieve them must be regulated by good taste, to give a pleasing consistency to the contour.

Louisa
Mistress of the Garderobe