There are two problems with grass clippings, both mentioned in previous posts.
First, clippings tend to stick together in clumps, making it very easy to eat. This can cause choke or colic due to eating too quickly.
Second, clumps of clippings start to ferment very quickly (basically biodegrading). The fermented product can kill horses. At this point its basically spoiled haylage. Properly prepared haylage is very healthy for horses, as is nicely dried hay, as is fresh grass. Unfortunately clippings don't fall into any of those catagories!
If you don't have clumps, or its mowed down and chopped up, or if the horses prefer the newly-exposed fresh grasses there is nothing to worry about. It would be nice to be able to pull horses off freshly mowed pasture for a day or two but in most cases that's not possible or nessesary.