They will only eat bark in winter unless you put something like chicken wire around it. They will definitely ear all the leaves and brake branches upto around 2 metres height.
Even 2 month old goat know exactly what to do. They bend the young trees to get to the crown and eat every single leaf!
If your trees are taller than 2-3 metres and thick enough that when a goat stands against it and it doesnt snap or bend you should be fine. My goats snapped some of my young fruit trees - almond, apples, pear, they wear really trying hard to get to the sweet chestnut but I protected it with a barrier made of 4 pallets
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If the tree is tall enough that should be fine, but beware If you have young trees that are not taller than a goat standing on two legs (2 metres!) They will still finish all the leaves that they can reach. Very very naughty.