That is a variety of Prickly Pear cactus. It is the only cactus that I know of that can survive our cold Wisconsin Winters. The reason you didn't see it inside the conservatory is because they have a large patch of it growing outdoors. It is edible and is often served in Mexican restaurants here. The type we have here gets gorgeous yellow flowers on it and blooms for a long time, although the blossoms only last one day
RE: Photo-essay of the Desert House