Natural materials are used in upholstery in much the same way as 'conventional' foam & padding, with the noted exception that the wool batting is not glued to the foam (as polyester batting is glued to urethane foam in conventional upholstery). Instead, the wool batting must be either sewn or stapled around the latex foam (see demo video here). It has a thin spun backing (see photo here) that makes this easy. You can purchase this same wool batting at DIY Natural Bedding.(Note: this is an affiliate link, which helps keep the Natural Upholstery website ad-free; we appreciate your support!)
Note: with the wool batting, the outer upholstery fabric will need to be lined with ticking fabric to prevent the wool fibers from traveling through to the surface of the upholstery (ticking fabric is not necessary with leather or other non-woven material).