I don't have any pasture and my goats are thriving on scrub and
trees. I have them free ranging over a large area, but I've also kept them in a small strawyard near the house, when I brought all their
feed to them, and they were happy there as well.
Some plants are better than others, and some are toxic to goats, so it's good to get an idea of what is growing, and also an idea of any mineral deficiencies in the soil, and the pH of the soil, as this will affect what nutrients are available to the goats in their feed.