I have field fence with electric on top on my personal farm and have fenced my horses away from it. I personally wouldn’t board my horses at a place with field fence. It is awful stuff and I had a couple horses injured – not wearing shoes – from tangling in it and getting a leg through the holes. Horrible. I am budgeting to replace mine this year. It is the thing I hate most about my farm.
If you run a interior fence as you describe, do it 6 feet away, not 2. they will still be able to kick into the field fence if it is that close.
If you have any doubts about the safety, I can send you some pics that will make your stomach turn…learn from my mistake! It is not at all the same as no climb, unfortunately.