I am considering this too. Get a really good portable electric fence and move them around the property to clean it out. However, many folks familiar with goats have said that sheep are less picky and will eat bushes and small trees that goats won’t be interested in. The problem with sheep is that we have large coyote packs running around here and some of them are about the same size as my German shepherd.
I may try out pigs and fence them in the woods a 1/4 acre at a time to see how they do. Supposedly they root up everything! They taste better than goats or sheep although some mutton dishes are mighty tasty.
Rolled shoulder with salt, pepper, thyme and mint jelly is paradise. The best thing ever.
You’re right about sheep being less picky. Sheep will even eat goatheads, which goats won’t touch. Goats are crazy. They’ll eat a shoe or a rope, but not goatheads. :) And sheep taste better IMHO.
If anyone’s wondering what goatheads are, it’s the nastiest plant I know of.