This is what I'm currently using on my sensitive skinned mare. Straight Air Flex Smart Cinch Weaver Leather (Supplies Tack - Saddle Accessories - Cinches)
ETA: I really like this cinch for her. I've tried mohair, alpaca, fleece, felt, and neoprene. None of them worked as well. She has not had any rubbing with this one, and that includes the trail ride we were on when I bought it. Hours of really big hills (we people from Kansas like to call them mountains) and it performed way better than I expected. I can't tell if it really is any cooler than standard neoprene, but I can tell the pressure is more evenly distributed that with other cinches I've tried.