A lot depends on the size of the tree, and if it will sprout from its
roots again if it's eaten. Small trees are likely to be eaten completely (but might come back up again once the goats are gone). Large trees not so much, but there is always the chance that they'll eat the bark.
Goats are more likely to eat bark if they have mineral deficiencies (especially copper), give your goats access to a mineral lick, and they'll be less likely to do this.
Keeping a close eye on them and moving them as soon as they start causing damage would also be a good plan.
Another thing to keep in mind is that goats are naturally browsers rather than grazers - when given the choice between trees and pasture, they'll often choose to eat the trees.
If you are designing the whole area from scratch, it might make sense to keep the trees in rows rather than scattered here and there, that way you can fence the whole rows off rather than individual trees.