You could try taking a net, removing the long strings for hanging (just use a carabiner to close it) and plop the whole thing into a large tire. If your horses don't pick it up and toss it around, it will stay put and serve the purpose. If they DO decide to play frisbee with it, you could tie it down inside the tire to a cinder block or something.
Then a freedom feeder clipped closed or "sewn" closed would work well. You could also try a cinch chix, but you'd have to ask about making those into a pillow. I think nibble nets may have a small hay pillow as well.
I have a barefoot full sized horse and a barefoot miniature donkey climbing all over a Cinch Chix net with no problem. The mini's hooves do not go through the net.
I do throw the rope over a barn rafter, and hike it up from time to time. If you don't, it will be an enormous mass of netting on the ground. However, I don't think that's a significant safety problem with barefoot horses -- just a messy, huge puddle of net.
We have used Nibblenets (the largest size) for over a year now. We don't have any minis, so I can't comment there, but one of the horses is a fox trotter with petite hooves. We have had no problems with them. In our herd of five, one has shoes.