Not too many people are even aware that there are such creatures as "hair sheep". Most people have only heard of, or seen, wool sheep. True, most sheep are wool sheep, but there are distinct advantages to having a sheep that has hair, much like a German Shepherd dog, rather than woolly locks.
The obvious advantage is that hair breeds do not need to be shorn. Shearing is very stressful on a sheep and often results in injury, in the form of nicks and cuts. Worse accidents have been known to happen due to the catching or incorrect handling, this would include things like broken legs or ribs.
The price of unfinished wool is relatively low compared to the effort involved and sometimes producers find they pay more for the shearer than they can sell the wool for. As such sometimes sheep are left with their wool on them, suffering in the heat for the summer. Hair sheep shed, some breeds may have small traces of wool but these are very minute and not worth trimming.
Hair sheep do not require their tails to be docked. This is a procedure done to lambs a few days after birth. The reason it is done is so their droppings do not cling to their tails. Docking always has a small risk of infection and, although brief, is certainly stressful on the little ones. As adults, a ewe with a long woolly tail covered in feces is putting her nursing lambs at risk of exposure to parasites. A ewe with a big woolly tail is less likely to be bred than a ewe who has had her tail docked, or than a hair sheep whose tail is therefore smaller in size.
Hair sheep are often smaller than wool sheep, making them more manageable to work with in terms of regular handling, such as worming, or feet trimming. Smaller animals work better for people who only want them for small hobby farms or as pets. The smaller size also makes them more efficient on food, requiring less feed over the winter.
Hair sheep are very attractive, some breeds resemble goats, but are much less destructive and not as apt to climb. Many look exotic, with large horns or mixed colors. If you want an unusual animal but cannot have exotic animals on your farm, a hair breed sheep may make the perfect alternative.
Hair breed sheep may be crossed with wool breed sheep. However one must be careful to use the larger ewes and the smaller ram. I have been breeding a Barbado hair sheep ram to many different wool breed ewes and been happy with the results, there are fewer lambing problems as the hair ram produces smaller lambs.
Hair breed sheep are noted for having a high resistance to internal parasites and because of their coats are more resistant to heat and humidity.
Most hair breed sheep are considered meat animals only, however a growing trend of keeping sheep as lawn, or pasture, control has resulted in many people wanting them as pets or living lawn ornaments. On hobby farms where uncontrolled pasture grass becomes a fire hazard, a hair breed sheep may be the ideal choice.
Some common breeds of hair sheep are: Barbado, Barbado Black Belly, Dorper, Kathadin, Painted Desert, and St Croix. The Sheep in the photo is a Barbado ewe.

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Some people have said hair sheep are more "wild" in nature than are wool breeds. I believe this is due to their wild look, and is not true of their behavior. I have owned several hair sheep and have not had an issue with them behaving wild. I have one ram who is harness trained and will follow me like a puppy, and many ewes who will eat out of my hand. I do not find them as aggressive at the feeder as the larger wool sheep, but in no way are they "wild". If you handle your sheep with kindness and teach them that you are their main source of getting food, they will not be frightened by you any more than another sheep would.