Most sheep graze, but these browse similar to a goat they just can't get as high on the trees and shrubs as I've never seen one standing on its hind legs to pull down branches. For me, that is a good thing, since the goats wiped out my fruit trees more than once! I laugh because they are always walking with their noses to the ground. They don't miss a thing. LOL
I have been really happy with my dorpers. They are not seasonal breeders so you can have 3 lamb crops in 2 years. They seem to be real easy breeders and mine have all been good mothers. Most of mine twin after the first pregnancy and they stay fat on beer cans. Best grass fed lamb I have ever eaten, very mild but flavorful. There are also other breeds of hair sheep, but I don't have any experience with them. I'm just totally sold on these guys
When I first bought my house it was empty for over 10 years, the yard was very over grown. My old Italian aunt said to me you need a goat, Being a city boy I thought crazy old lady. Many years later I read how good goats are for clearing brush. Looking back many times older people where right I was just young and dumb.