In general, parasols are used in times and places where
pale skin is part of the
beauty ideal, which is the reason why they're not usually used by men - openly caring for one's looks is
unmanly.
Parasols were probably most popular in late medieval and early modern times, when pale skin was not just considered beautiful, but also a status symbol (perhaps these are one and the same in this instance), because it meant that you didn't have to spend time on the fields working (which was, at that time, by far the most common form of work).
Less well-known is the fact that parasols are in wide use in current-day Japan, again because pale skin is considered beautiful by many people. On a sunny day on Tokyo, about a third of the women (especially those over thirty; tans are quite in among the youngsters) you see walking down the street will be carrying parasols or wearing wide-brimmed hats.