Hi newbi here

[Mini Horses]

They usually have trays under wire to catch droppings. That waste is good in a garden. Ya need a lid -- they jump out

 

[Baymule]

Look into rabbit cages with a tray under the bottom wire.
Litter will be thrown all over the place, so not good.
Puppy pads will be chewed and at least some eaten, also not good.