Baymule said it ALL --- P I G S R O O T !!!
So, larger pig, larger hole. They love the hole of water as they cannot sweat and it cools them, mud keeps bugs off. Other than that, they love roots of plants (that is why they leave a moonscape if not rotated) and the grubs, moles, etc that they find.
My AGH will stand and actually eat the grass just like any other grazer but, soon decide they want dessert & root. If you have room to them move them before it gets too bad, you can disc, reseed, etc. Obviously they will get rid of some growth because of the root thing -- so, use & move. The larger the pasture, the less deep rooting you will see. BUT I have had 2 of mine go into a space until I caught them about an hr later and it looked like I had done a fast run with a tiller! (that's why they used hog nose rings in past)
If you keep their fav spot wet, they like to return there -- & will make it bigger/deeper over time. But it does keep the huge hole area limited in number somewhat

There will still be smaller, shallower ones but, they can be navigated by the disc. The wallow? You need several loaders of fill.....
That curly coat is cute. Are these full sized hogs?