The fabric may go under different names, Shade Cloth, mesh, when you hunt for it. Farm-Tec offers quite a variety of the mesh type fabrics, made up in sizes for immediate uses.
I purchased a “mesh tarp” recently from Harbor Freight, to try using as a shade cloth over one end of the barn where I park the tractor. The orange is fading with hard sunshine on it every day, so I thought I would try the inexpensive mesh tarp there, to keep sun off the tractor. It is a rather fine mesh, so I am not sure if breezes will get thru for fresh air or not. It is fairly solid, so I hope the mesh fabric will stay down in breezes going thru the barn, not get to flapping in the wind of a storm.
I would go with shade cloth for horse barns, stalls, where you want air movement. They come in a bigger mesh than my tarp has, still cast a good shade, for keeping the animals cooled off. I got to see this in action at our Fair, when shade cloth got tacked up over the cow shed open sides, across the windows of the sheep barn, yet still let in a good air movement for cooling, while keeping things darker inside.
Check out the Farm-Tec site, they have a big variety of selections, finished and unfinished sizes of shade cloth available. Harbor Freight also has these mesh tarps, pretty inexpensive for a plastic type mesh. Not the same stuff as the shade cloth fabrics. But their tarps are all finished, have grommet holes already in them, various sizes, so could be a cheap fabric to try. Just not sure the moving breezes would get thru as easily with tighter mesh design, than shade cloth options.