We bordered a preserved wood lot on one side of our last place with some poplar trees being an easy three feet in diameter along with various oaks, etc. For a bit of extra insurance, I used those two piece galvanized springs on each row. On the occasion that something fell, I lost plastic clips and staples but once I had the tree cut off of the fence the tensile wire always sprang back up.
I'm not sure you need to truly buy high tensile fence, but rather run a high tensile wire above what ever fence you install. Run that top wire with a spring and tensioner and you should be fine. That's what I do with my fence. I actually ran 48" tall 2" x 4" woven wire fence with a high tensile 12.5ga. twisted smooth strand at the bottom that I hog ring the fence to , this keeps animals from pushing under it, I run a second high tensile 12.5 ga smooth twisted wire at the fence top that I hog ring the top of the fence to and then I run a third high tensile 12.5ga smooth twisted 2-3 " above that. If I need a hot wire, I can use the insulated t-pole standoffs between the second and third wire at the top of the fence.
I put the t-posts 8' apart and put a rigid pipe line post every 5 t-posts. I bought 200' rolls of woven fence and installed a welded pipe H (actually 2 posts and a top and bottom rail) that I used to pull the wire tight.
I've seen salvaged cable for sale on craigslist. You could run that above the wire fence and I've seen the heavy springs for sale at the metal supply places. That would hold up to any tree branches falling.
These are my two favorite tools for doing fencing 3-hole wire twister
I modified mine by cutting 1/2" off the handle and drilling the middle hole larger so it will work better for the 2" x 4" woven fence
A few years ago when I was checking out fencing I went to the New Braunfels Stay Tuff plant and offices. Good people and a good system. If you have any doubts about it you should drop by and visit the plant.