With only two horses on a round bale, unless you're able to place it under any man made or natural shelter, the hay may not weather well during rainy periods so even with a 500 pound round bale you may have a lot of waste. I would consider where you want to put the hay and if you can "park" it under any type of shelter that will be beneficial.
If the two horses have different dietary needs, I.e., if your pony is prone to overweight and founder, the type of hay you buy may work well for one horse and not the other. Since you're the one feeding, if you find that your pony's getting too heavy being free-fed, even in Winter, you can always cover the round bales, store them outside the pasture and pitchfork their feedings two or 3 times a day. I personally like having free choice hay in the Winter since it helps them stay warm.
As for the two-year old hay, if it was put up nicely, was good quality to start, clean of mold, dirt, animal droppings etcetera, and kept stored indoors, there's certainly nothing wrong with feeding it.
I realize your vet said it's not possible for a horse to founder on hay, but that unfortunately is far from correct. Every horse and pony is unique and I would keep a close watch if he's prone to founder, regardless of the time of year. Also, grasses can be high in protein as well as contain clover and alfalfa which can founder a prone horse or pony. Some orchard grass, for example, can be higher in protein than alfalfa. All depends where and who you buy from.