Hair Sheep as Lawn Mowers?

I've been working on a 5 acre lot I intend on living in, and I like to plan way in advance for what I plan to keep.  I'm in the middle of fencing off the property now, but I'm starting to realize I may not be able to stock everything Id like to.  My ideal situation would be to have 4 hair sheep and a breeding pair of American Guinea hogs on the lot, but I'm thinking the land will only be able to provide for one or the other if my goal is to have the pasture feed them.  I'm leaning more towards AGH, but I thought I would see how viable it would be to keep 4-5 hair sheep on about 4.5 acres with the main goal of keeping the pasture at an appropriate length, secondary goal for fun, and last goal for meat.  I'm thinking AGH may be more fun, but I'm very concerned with them destroying the land and rooting up the pasture and making wallows where I do not want them. Sheep seem to be easier.  I plan to rotate between 5 pastures around .7-1 acre on a weekly basis, with the goal of minimal supplementation.  Is this a realistic goal for hair sheep?  

I have hair sheep and they mow 99% in my area. The only thing that gets out of hand is dandelions and a native lantana(perennial, have to dig it up). I can manage the dandelions with a cordless weedeater before they take control of pasture. It is amazing the variety they eat. Stuff that horses and cows will not eat. I say go for it.

Sounds good to me, and I have both AGH and hair sheep. The sheep are easier, but I do love my AGH pork, so I can't choose between the two myself. You would have to supplement the AGH with a little grain. I've seen people try to raise them on pasture alone, and it was not good.

As someone who has both, do you think agh would be able to keep the grass mowed without rooting too much?

If you have tons of lush grass, they will eat it. But in the fall when the grass stops growing, they start rooting. The other thing is that if they smell nuts, they will root. So, they root around all of our trees that produce nuts, which includes oaks and hickories here. You can see the rooting stops at the edge of the tree's dripline.