Go with Oilskin it's still cotton and breaths but it is near waterproof and windproof.
Not bad if it has a removable or no liner, whole concept of a riding jacket is to provide some extra warmth and wind protection. In the heat of the noon day sun everything is hot except maybe a spandex onesie, that's cool except for the back protector which is as hot as wearing a backpack. Unless the back protector is filled with cold water and that would be very cool!Are waxed cotton not very warm?