As a general rule: wool rocks! But technically, all wool yarns can shed due to the structure of the fiber. Good wool sheds less than not so great wool.

But the natural shedding that can occur from wool yarns, is typically not terribly noticeable. So if you are seeing an abundance of fibers coming from your rug, it's probably due to something other than nature of wool yarns. 

If you have a brand new rug, those cloudy tufts can be cut fibers that were embedded into the face of the rug. When rugs are made, the wool yarns are often much longer than the pile of the finished rug. At the end of the rug making process, the yarns are cut to the desired pile height or rug thickness. It's like a big haircut for your rug. Cutting the pile can leave little pieces of wool fiber in the rug. Over time, these pieces work their way out of the carpet. If you have a brand new rug, this could be what you are experiencing. Worry not! Shedding of brand new rugs should subside within the first six months or so.  

If your rug is not new and suddenly you notice wool fibers scattered on the floor, it’s almost certainly a tufted rug. In the thousands-year old rug making trade, rug tufting is relatively new. Instead of tying knots on a loom (a slow, careful, and arduous process), the rug-maker uses a tufting gun that shoots the wool fibers into cloth backing. This is a much much faster process. Once the pattern is finished, a piece of fabric is glued on the back of the rug to secure the wool fibers in place. So essentially, the rug yarns are glued down. In time (depending on the quality of the glue), the glue can start to fail causing the rug to start shedding. At the same time, you might notice some white powdery substance coming from your rug, which would be the glue itself, now dry.