Your best bet would be a skid-steer loader or articulated construction loader, if moving 1-ton bales is the main task. Those have the lift capacity and counterbalance to move them safely (obviously some models of each are below that lift capacity, but many models have it). I'm not referring to huge articulated loaders like at gravel pits, but rather smaller models like Kubota makes, often seen at landscape supply places. A tele-handler would also work well but the price and limited availability used would probably make that out of the question. A used construction type backhoe-loader might be another option, either if you have a use for the backhoe or if you find a good deal with or without a backhoe.
It certainly CAN be done with a farm type tractor, but you will need a very big tractor. I move 800-1000lb round bales with my JD 5105, 50-hp utility tractor. I would not recommend anything smaller for round bales of that size. This tractor has rated FEL lift of 2100lbs to full height and about 3500lbs to 59". FEL lift has not been an issue, but with balance and all I wouldn't go any smaller. I have filled rear tires for 1500lbs and I always have a heavy implement on the back (usually a 800+ lb disk or a 700+ lb mower) when moving the round bales. Heaviest load I've ever lifted is approximately 1500lbs in the bucket and I could really feel it, even with all that counterweight. I could move something weighing 2000lbs once a year, but I think it would be unsafe, or at best marginal, to do it regularly.
Now I realize you're using large square bales, not large rounds. The weight and the bulk are both issues. Because of the bulk, the weight will be well, well in front of your loader pivot pins, and even in front of the common 500mm forward measurement. You would probably need something that can lift at least 2500lbs at 500mm forward, and you would be much better off and safer having a margin for error in both weight and positioning, with a rating more like 3000lbs at 500mm forward. No CUT has this high a rating, and in fact that puts you into the upper end of the utility class tractors. So in farm tractors you're probably looking at a 70-100hp tractor to safely operate a loader with the power you need.
Now, if you're planning to run a 15' mower or do serious tillage, such a size tractor would be great. But if moving the bales is the main big task, you would likely be better off with one of the construction loaders noted above.