In the wild, horses mark territory by pooping and peeing in the same places. It tells other horses " this is our range". Our stallion from the west, pastures of 5000 acres, would always poop in the same corners of his fields. There was a regular stack of manure here in each corner location of his much smaller pasture. He actually backed up to the pile to make sure it piled up higher each day! His gelding buddy also used those locations to poop, then stallion pooped on top of it. It was what they were used to doing as herd horses out west, using instinct, observation of other herd members for their guide.
I like horses using the same locations to poop, it leaves all the other areas for grazing. They don’t eat where they poop. I drag my fields to break up poop, spread the organic matter to enrich the soil and plants as part of field rotational grazing… A years worth of pasture mowing is supposed to equal an application of fertilizer, no extra cost to you! Cutting makes the grass grow back better by keeping the leaves short. Hauling manure out of paddocks, pastures, removes all those nutrients from soil use, so you will need more fertilizer to keep the grasses growing well, being nutritious for the animals. Like folks who just cut hay, never fertilize. They are hauling away the nutrition, in time the hay field is far less productive, worthless as feed because all the soil nutrients are gone.
I have never had manure balls stay hard, refusing to break up. Is it a local problem with weather cooking them? I do tie on some old tires to our chain harrow to keep the teeth firmly on the ground when dragging fields. Maybe some tire weight on your drag would be helpful in breaking up hard manure balls.