Depending on the part of Missouri, it's really rocky and the topsoil can be thin, so the grass quality may not be so good, or will require maintenance. I have about 3 acres of grass and 3 acres of wooded land in the Ozarks (very rocky), and it will only graze an animal from April-maybe July without supplementation. If I feed and rotate, I can get through most of the warm season with some grazing. That would point to 3 acres/horse not being enough in some areas.
The barn I board at has more topsoil and better quality pasture and they probably have about 3-4 acres/horse and are able to use grass as the sole forage through most of the warm season. They do, however, rotate, fertilize, and reseed as necessary. I think they spend quite a bit of money on the pastures, honestly, and are lucky to be in a really good spot.
To be on the safe side, I would recommend 20 acres for two horses here. The rule of thumb is less, but I don't think you can realistically not feed at all AND not rotate turnouts or do pasture maintenance with less. You'll still at least have to bush hog to control weeds, too.
Tug on anything at all and you'll find it connected to everything else in the universe.~John Muir