Horses eat grass, and they eat hay - but they cannot consume grass in the stage in between. The main reason for this is that cut grass starts to ferment (which is why they feel warm to touch), and the fermentation process will continue inside a horse's gut, which is extremely dangerous. Grass cuttings will release gases which cause the gut to expand and often rupture as this gas cannot be released. Many horses have died as a result of members of the public putting lawn cuttings over the fence into horses' paddocks.
In addition to this, grass cuttings / garden waste can be extremely dangerous for the following reasons;
You can find out more information about the dangers of cut grass here
*Note - Not to be confused with grass sickness which is quite different.