This image depicts an essentially ages old process of collecting hay and loading on a wagon. This drawing at the LoC has a caption of foraging for hay in Virginia. Note that forage as a verb means to look for food for both men and animals, while forage as a noun is the hay and grain used to feed animals. By the time of the civil war, farmers and hay distributors made hay bales using horse powered presses as I described here. They shipped the bales with concentrated hay from farms to urban areas.
During the civil war, the farms in eastern Pennsylvania produced prodigious quantity of hay, according to Hess in his book, "Civil War Logistics." The US Quartermaster Corps purchased bulk hay and shipped it to the Army. In the case of the Army of Potomac, the hay came by ship and barge. If you look at the three-masted schooner in the background of this image from City Point you will see it is fully loaded with hay.
The Merritt map of City Point shows a wharf labeled as "Forage Wharf." This implies a dedicated place to transload and store hay.
To transship the hay to the hungry animals in the front lines the Army used wagons and railroad cars. In the photo of City Point at the left we can see a line of wagons proceeding to an area where piles of hay bales are stored. Look behind the trees on the right side to see the hay bales.
If you look closely at the image below of the Aquia Landing, you can see a flat car loaded with hay bales on the right side of the image to the left of the locomotive.
I have posted other pictures of hay bales on railroad cars such as here. Armed with this knowledge, we can proceed with adding hay bales to our civil war railroad cars knowing we are on the right track.