We tend to have an image of clover being a good plant. The picture of a cow or a horse up to their ankles in clover is common.
However, clover can often be too rich for horses, and should generally not be fed to ponies, especially in the spring. Clover just has a lot of sugar in it. Because of this a lot of people in the UK (where most people ride ponies) remove clover or fence horses away from it in the spring.
In the US and Canada, red and alsike clover are associated with poisonings, but it's not the clover itself that's toxic - it's mold that grows on it. Mowing can remove the mold. Red clover poisoning is mild - it just makes the horse slobber. Alsike clover poisoning can cause all kinds of problems, including liver problems. Oh, and both can, uh, give them diarrhea.
So, clover is not great for horses, but if it's mold free it's fine (and they like it) in moderation.