Yes, it's a turned out tire. You could really use any tire you like, then just take measurements to decide how much netting and lacing you'd need.
Someone also asked about preventing horses from flipping it over. In my experience, I've never had a horse flip a tire over, especially not this size. However, there are a few simple fixes if you're worried about it. First, there is actually a pretty big lip on each side of the turned out tire. The ones in these pictures have it trimmed off on the top, but there's about a foot or so all the way around that actually sits on the ground. A friend of mine just drilled holes in the bottom and bolted the tire down with rebar. Second, you could attach something on the bottom, like a piece of wood or even a second net. You could pull the net tight, but if you kept it loose or even just did the second side like the first, you could use the tire both ways. Because the holes are so small, I really don't get a lot of hay falling out. However, I watched both my horses eat a good meal out of it today! It's cool to see them work the hay out and they really get the method down to eat after a while.