Sorry I don’t recall seeing any specific mention of whether hogs eat ants or not, just that they do eat insects.
Not sure why the ants would be attracted to the hog house, unless you’ve had something sweet in it. But once you’ve pressure sprayed the ants away, you could try to clean the hog house with boiling water, making sure it gets in the joints of the wood, which is the method recommended to kill parasite eggs (ticks/fleas).
I agree – definitely no to ant killer. Not only bad for the hogs, but may also deprive you of the vist from the green woodpecker, which must be lovely to see.
If all else fails, maybe a new hog feeding box?! That’s what I had to do years ago when a hog decided to build a nest in one!
Good luck and happy hog watching.