Sheep are grazers, not browsers; which is why goats are the ones you want for a burr problem. I don't have a single tumbleweed left in my goat's pen, but we have to seriously modify our pastures in order to make them safer for the goats; not only can they escape, but DOGS can get in!
I honestly don't worry so much about escaping goats, because they are such personable little critters, especially if you get one that has been socialized alot; all three of mine LOVE attention, and only one has been bottle fed. I worry more about neighborhood dogs that are running at large and looking for something to do...even though a goat will defend itself, it can't stand up for itself against a large dog or more than one.
"The ideal horseman has the courage of a lion, the patience of a saint, and the hands of a woman..."