Horses have been made quite sick by well meaning suburbanites throwing lawn clippings into their pasture.
First of all, lawn clippings contain a high level of the wrong kind of carbohydrates. Horses ferment their food. If they ferment it too quickly, then they can get acid in their gut - basically indigestion - which can then cause laminitis.
Second of all, they tend to bolt them, which can result in food getting stuck in their throat - choke.
Third of all, lawn clippings may contain plants toxic to horses. The overall smell of the cut grass will mask the smell of individual plants...
Fourth of all, toxic weed killers may have been used on the grass.
So, nope. Horses should never be fed (or allowed access to) lawn clippings.