I would save it. Dry peat moss repels water and I think makes a much better soil amendment.

Peat moss can be, and has been, used for mulch, just be aware that peat moss used that way tends to be hydrophobic, water repelling. When dry it takes peat moss a long time to accept and/or allow water to flow through it, but then bare soil can do the same thing.
Like any organic matterial placed on top of soil peat moss can, if enough is placed down, aid in keeping soil moisture from evaporating, aid in keeping the soil cooler, and aid in suppressing unwanted plant growth, "weeds". Peat moss can even, eventually, add some organic matter to your soil when used as mulch.