In this country, we always used to feed loose hay on what we called "hay sleds," even though they had four wheels instead of runners. Some folks called them "low-boys." They were basically built with steel I beams with a wooden platform. The platform tipped, so one side completely touched the ground. To load, the sled would be pulled up alongside a four to six ton hay stack. The team or tractor would be disconnected from the tongue of the sled and maneuvered around to the back of the sled and pointed perpendicular to the sled. A chain from the front of the sled would go around the stack and then be hooked to the team or tractor. Then the stack would be pulled onto the tilted sled.
Usually just half of the stack would be pulled on to start with. After this hay was fed, you came back to load the bottom part, called the stackbutt. If you used a tractor, sometimes you could cheat and use a dozer to push the stackbutt onto the sled. If using a team, there was quite a trick to loading and it involved two chains. The first chain was put right down on the ground and almost encouraged to cut under just a bit. You didn't dare keep pulling with just one chain because the hay would tear all apart. After the team had just tightened the chain in the cutting under postition, a second chain would be placed around the stack, about a foot above the first chain. The chains would be tied so they had equal pulling pressure, and the stackbutt could be easily pulled onto the sled just about as slick as a chain mover could have done it. Not everyone knew this trick, and I didn't learn it until riding around with Buck Buckles who still uses a six-horse abreast hitch.
Back to loading round bales, they can be cabled on in much the same way as I have described loading loose hay. If things are done just right, the bale tips strategically so it lands on end. It is fairly easy to cable two bales onto a haysled, both standing on end. Then the strings can be cut, and the bales pitched off with a common pitchfork, or better yet a curved drag-fork. I've fed a lot of hay this way, and it doesn't work too badly.
Scott Manufacturing from Gordon, Nebraska makes a nifty two-wheeled cart that has two winches. It hauls and unrolls one bale at a time, and can be pulled with a team, pickup, or tractor. These are priced at around $2000. I just looked on their website, but they don't have this cart pictured. It does sure look like it would work though.