If you fence the thing in goats are not a bad idea.
Realize that you can't just plop in a dozen goats and walk away, and come back next year to find 2 dozen goats.
You will need to provide water source, shelter (3ft by 5ft per goat, three walls and a roof is sufficient), and checking in on them twice a day, at least briefly to make sure there are none that have gotten through a hole in the fence, walking with a limp, or any other issue.
Goats might gnaw very small saplings, but won't take down trees thicker than your forearm. They'll eat the foliage, which may kill it.
Goats will be a lot of work in the long run. This is why there are actually companies that will do this for you with goats.
However, unless you are fixated on goats, just go rent a forestry mower or forestry mulcher and get it done, or hire a guy who has one to get it done.