That is a real good idea. I think that would be best vs removal.
As a former landscape designer, IMO the main thing missing from this property is *landscaping*, especially for a property of this caliber. Not talking about the immediate yard, which looks okay aside from the weird snake-like hedge. But the fields are stark and bare, and that makes the fence stand out like a sore thumb. Looks like the place was designed by an OCD neatnik. It lacks grace and charm.
The challenge is the sheer length of the fence lines. The key is to break it up. Start with a tree at each corner, and at each "kink." The barn could also benefit from a tree or two (horses like a little shade). There is a noticeable lack of gates, which are handy of course, and also a great way to break up the long fence lines. If you want to throw down a little money, put stone columns on either side of the main gates. Flank those with some hedges or other plantings and you've broken up the long fence lines, and created attractive focal points in keeping with the formality of the overall property. There should be a nice pathway from the house to the paddocks and barn. Take a look at some pics of classic horse farms for ideas.
As a horseperson, the strangest things are the weirdly curving drive to the barn, and how do you turn a horse trailer or hay-truck around? Small detail: I've never seen a rounded paddock, but maybe that's a "thing" now.

If you want to tear something down, those could be made a lot more practical and "workmanlike."
So I completely understand why your wife doesn't like the fencing, but it can probably be greatly improved short of total removal and replacement. Still think a realtor's input could be valuable. You and I may be picky, but how discriminating are your potential buyers?
(If you call in a landscaper or GC, have them do a design on paper (or computer) before you commit. Most landscapers and GCs are lousy designers.)