Goats are browsers, they will eat wisteria. To reduce wisteria, you need lots of goats, and little choice. You need lots of goats because in quantity, wisteria can be harmful to them - lots of goats spreads the harm (and reduces the time needed to reduce the wisteria to very little on property). Think "rent a herd".
If you happen to have a few goats, and a little wisteria, and a lot of other choices, your goats will nibble on it from time to time - particularly the dry brown leaves and will help control its growth but if you want it gone, you will be removing it, not the goats.