You can soak their grain so they have to ingest extra water, add flavour to their water so that they want to drink it (like apple juice), give them electrolytes (or add salt to their grain) so that they get thirsty and drink. You can also trick horses that don't want to drink to ingest some water by floating thinks like apples in their water buckets (make sure to figure out what size they need so they don't choke). Often they won't be able to grab the apples (like humans that go bobbing for apples) but still get mouthfulls of water. Even if they spit it out, they'll get SOME (even if it's a very small amount).
By the gluttony! My horse doesn't drink at all, I put 1L of mash in a big bucket and I full it with water (around 8L). The mash stays in the deep and my horse drinks all the water to reach the deep and so the mash. I give him every evening to be sure that he drink a little bit... :)