Ice packs made from plastic bags or cloth quickly get damp and messy as the ice inside melts. Try disposable nappies instead; they'll stay cool to the touch and the lining will absorb the condensation.
Photo by Nate Ritter.
Parent Hacks suggests pouring ice in between the layers of the nappy, folding the top over, and then securing the pack with the tabs on the sides. You wind up with a comfortable ice pack that stays dry and clean thanks to the absorbent lining.
If you have newborns or toddlers, it's worth a try, and its definitely cleaner than a bag of frozen vegetables from the freezer.
Make Absorbent Ice Packs Out of Disposable Diapers [Parent Hacks]