Wire fencing is one of the most common types of fencing in North American, yet it is also the most dangerous for livestock, including horses! I can tell y'all this from experience (not a very pleasant experience). It is not an uncommon occurrence that a horse will try to reach to the other side of the fence and end up getting something caught on it. It may a hoof or an ear, but either way, it's not pleasant if the fence is rusty and your horse scratches himself on it. If that happens, it would be a good idea to consider getting your horse a tetanus shot.
My LBI pony did exactly that, reached to the other side of the fence and tore the edge of his nose.
So please, do your best to avoid or replace any wire fencing you already have.