BH and several of his neighbours got through one of those really snowy winters using up some well-stored 4-year old hay he had in the Dutch barn. It was readily scoffed by Texel type commercial sheep and our native ponies alike, with no ill effects.
So yes, open a bale, look to see if it's dusty and whether there's any musty smell. If your senses don't tell you it's no good, spread a segment in a field in front of a couple of cows, or some hungry sheep, and see what happens. Experienced cattle (hence I suggested cows not bullocks or heifers) are great for finding the good stuff and leaving the rubbish, so if there's any good in there they'll pick it out and leave the rest to disperse in the wind / rot back down into the soil. Sheep won't eat bad hay, end of. They'd rather die. So if they're hungry and won't eat it, it's not good for sheep. (Although of course some sheep are just awkward cusses and won't eat it cos it's different
)
If sheep will eat it, horses probably will too. At least, fat greedy native ponies will. Feed outside so that any dust disperses. With natives, you're often looking for hay with low feed value to give them bulk without them slabbing on the weight, so you might even find there's a local market for the stuff!