I always feed greens fresh and if they need to be around for a few hours, I spread them out. Remember, heaped greens soon start to ferment and can kill young rabbits from my own experience. Wilted greens will not hurt as long as they are not yellowing. I do not put greens on the floor, rabbits will step on it, the food will get spoiled and contaminated by urine and rabbit feces.
Much better is to bundle grass and hang it up with wire or rope or put it behind a rake. If you feed cabbage or cabbage leaves feed them in very small amounts as they tend to be very strong and too much can kill young rabbits. Before I feed new greens I remove the left overs from the previous feeding. It is much better to feed 3 to 4 times per day instead of once.