When I was 9 or 10, I put a tin can on a tree with a nail.
I was reamed up & down, inside & out by both mom & dad! Man, a person _never_ puts metal into a tree! That lesson was well learned.
We make fire wood from our trees, and at one time had a lot of trees cut into lumber. Metal is a bad, bad, bad thing on a tree! Can actually kill people. Costs thousands to a lumber cutter.
So, I just shutter at the thought of putting nails, screws, or holes with wire in your tree.
In addition, to me personally, it would look really ugly to have the fence attached to the tree. Any other suggestion here would look much better to me. (I guess the folks made quite an impression on this 10 year old!)
I like the (real or fake) gate idea someone had. If looks are important, you could box that corner out, make a square around the tree with 3 corner posts - always looks good if you keep it square, I do understand about just cutting across the corner not being so good. You can do some flower bed or shrubs in the corner to make quite a centerpiece out of it.
Your tree, so don't let my ranting & ravig bother you.
(But, don't nail to it - please.....
On a side note, have you checked local laws on setbacks, especially from the road? Neighbor had to pull his fence & redo it 15 feet back from the easement line. And this is about as rural as it gets. Just a thought.
--->Paul