It seems my lovable goats have made an old apple tree naked.

I know not everyone cares about their trees, and this one was expendable since it had already fallen over. However, there are some good old apple trees and some native trees I'd rather keep.

My question is:
1. Are there meaningful deterrents?
I do need to do some chicken wire anyway to deter beavers on some trees. Will it help?
I feed them grain and hay - is their diet wrong?
2. Or should I not plan on giving them access to trees I care about.
I was considering extending their wire fence to cover a much larger area and give them range to four acres. However, it is also possible to give them up to 2 acres of mostly weeds/grass and exclude most trees. However, this restricts their access to some invasive blackberries that would be good for them to eat.

Thoughts?

I have 4 wethers on an apple farm, and so I can say for certain that keeping the goats under the apple trees is a challenge. First of all, the chicken wire works, sometimes you have to use two layers because they will nibble little bites in between the wire. Or use aviary wire which is a smaller opening, but is wicked expensive. Don't wrap the chicken wire tight, or you will girdle the tree and they will be able to nibble easier in between the wires. You will have to be really persistent, as they usually have all day to do nothing but figure out where else they can eat the bark.
Second BIG problem I've had- the little pigs ate so many fallen apples last year they got extremely fat and one got kind of bloated and drunk, and was like a mean crack addict untill he detoxed from the apple glut. They had learned to shake the tree branches to make the apples fall. I would highly recommend not including your apple trees in your pasture if you have that choice. I have to put livestock pannels around all the apple trees in their pasture in the fruit season.

2. Or should I not plan on giving them access to trees I care about.
This is what I have done- just can't give them access- they're browsers.
I make sure when I go up the canyon fishing that I bring them back some fallen timber. The only time I give my boys grain anymore is as a treat to keep them occupied while I trim hooves.

Goats are great for clearing brush and trees, they love them tasty leaves and bark. I've found that the tree you're trying to protect the most, that's usually their favorite!!