I love the box slow feeder idea, but I wouldn't be using any metal fencing or anything like that. There's actually nylon webbing that you can buy and you can just sndwich that between two pieces of wood to use as a net for them to eat out of. The NIBBLENET ® Slow Feeder Hay Bags - thenibblenet.com - Official website of The NIBBLENET ® Slow feeder Hay Bag - Slow Feed Hay Bags for Horses
This is an example of what I'm talking about, but I wouldn't buy from there. Super super expensive. You can find your own nylon webbing and if you have a heavy duty sewing machine, sew it together yourself.
As for me, I use hay bags I bought online. They have the nylon webbing for the front and are backed by canvas material. They're super heavy duty, sit outside 24/7 and haven't shown any signs of wear or tear for the past couple months I've had these. I used to use a different brand, Derby, but the outside of the canvas was a cloth material and it would bleach and crack and the inside would peel after about a month. These new bags are the nylon canvas only and have held up great so far. They hold 2 big flakes(about ten pounds) but I could stuff more in there if I wanted to. I set out 3 bags for my fatties, about 25 pounds of hay, and that will last my two boys twelve hours! https://www.horseloverz.com/product/...ay-feeder.html
ETA: The hay should at least be at chest level. Just like the reasons you stated Katie, and also for choking hazards. When a horse is eating off the ground or at or below chest level, their throats produce more saliva making things go down the throat easier. Up above chest level, they don't produce as much so things can more easily get stuck in their throat. I feed my boys from buckets on the ground then put their hay bags at chest level.