When sheep break their horns it can be serious. They could bleed to death, or they could suffer from the result of infection, or flies. As well tetanus can be a concern.
When we had some Jabob ewe lambs, one seemed prone to always knocking one of her horns off, causing bleeding, and worry. If a sheep breaks a small horn treating with Iodine, or any other product you have for bleeding and/or infection, is a good idea. You can apply something to keep the flies away too but keep it out of the wound unless instructed otherwise as per your veterinarian (not all products can be used on sheep). Make sure to stop the bleeding.
If the sheep does go off its feed, and starts grinding its teeth - call a vet. If the horn was large and was broken right off (say on a Jacob, or Barbado ram) call a veterinarian immediately!
We just had a ram lamb, with small horn buds, knock one of the tips of his horns off. We were separating the lambs from the ewes and accidents like this are likely to happen with lambs trying to get back to their moms.
We treated with iodine, and are letting the wound heal on its own otherwise - exposed to the air. It is still too cold for flies here, so we are not worried about that.
This picture was taken about 4 hours after the injury happened, it was bright red when it happened, but who thinks of taking a picture then? You can see how small the other horn is, only about 2 inches (5cm). The injured horn may be sore for a few days, but this little ram lamb should be fine and will continue to grow a horn in spite of the setback.