I don't know if it is all that bad that they eat moldy hay. I do know that when they are eating it, they will inhale the spores. That can easily cause heaves, which happened to one of our horses when he was boarded. Posted via Mobile Device
You can also get rid of some of the dust by wetting the hay before feeding it. There are a few horses at my barn that are very sensitive to dusty hay, so they have a big plastic tub that we toss the hay in, pour in a few buckets of water and drain before feeding.
If the hay is just brownish, it's ok to feed. Mold has a distinct odor. If too damp it will also have lots of white specs. Hay that is turning yellow will smell like corn. Don't feed either but save it for a summer smudge to drive the bugs away. Don't put hay close to your face to smell for molds. The molds are very harmful in the lungs. If horses have plenty of good hay they won't touch the moldy hay if accidently fed.