Bepp, I don't think you are in danger of doing anything to hurt your parents' horses with the hay you feed them. Dry, wet, old, new, damp, whatever hay, plastic bags, etc. aren't going to put them in the grave. You obviously want to use common sense and not purposely feed them hay that has visibly gone bad (lots of mold, rotting, etc.).
I hear lots of stuff about "that'll make your horses sick", etc. Also, you have to have special "horse fencing" or your horse will will hurt himself and die. I believe horses are more hardy animals than some people give them credit. You can literally spend a fortune making special environments for horses. Our Tennessee Walking Horse ran with our cows, ate the same stuff the cows ate, and used the same fences. We had no problems. She never got sick and never hurt herself on the barbed wire fences. Horses are smart animals, much smarter than cows.
If you have $100K+ prize horses, then maybe you don't want to risk a horse's scratching his neck on a barbed wire and maybe don't want to feed him hay from a round bale. But for the average horse you use mainly for riding on trails, etc., I'd treat 'em just like cows and not loose a moment's sleep.
I realize my suggestions run counter to what you commonly hear. However, there are a lot of broke horse people who end up spending a mint by following the advice of the "so called" experts. I have difficulty spending $20K to take care of a $2000 horse.
For a 3 acre lot, the cheapest thing you can do is either get someone to bale it or just buy hay from someone else. My dad hires out the hay making on his 110 acres because it's cheaper than doing it himself. In fact, depending on the price of hay, some years he justs buys the hay from someone else and uses his fields for pasture.
Just my opinion.
Obed