Weather in Dubai is pleasant (a slightly stuffy 80F, with a light breeze off the sea), but not pleasant enough that I'd want to walk around in this. The men get to wear white robes, but the women all wear black. I can only assume that this leads to truly epic cases of swamp-***.
Also, the taxi kiosk at the airport has a separate station for "Ladies' Taxis," cabs with pink tops and female drivers. Females aren't required to use ladies' taxis (i.e. Westerners), but I get the feeling that it is strongly encouraged by local customs for local women.
Feminists, to arms!!