The horn and the radiating diaphragm are two separate things. The diaphragm can be made of any material, just like a direct radiating speaker. You'll see paper, plastic, cloth, metal and composites.Compression horns put more pressure on the radiating diaphragm than it would have without the compression chamber. There is a constriction in area between the diaphragm and the horn throat which causes pressure to be higher than it would be in free air or mounted on a baffle. So for this reason, the radiating membranes on drivers that are designed to be used on horns are often made more rigid than general purpose drivers.