I would love to be able to compost it but, unfortunately, with two dogs around I don't, for fear they might get into it. There's a lot of alcohol in those leftover skins, and grapes aren't really good for dogs anyway.
What I sometimes do is add a few pounds of the spent grape skins into fruit wine batches to give them a little extra structure and color. For example, although you would think it would be bright red, strawberries actually make a very light colored wine - almost clear. By adding some of the spent grape skins in while it's fermenting, it makes it look more like the natural color of a strawberry without changing the flavor.
Beyond that, they just go into the garbage.