I just went to Blizzard Beach on 11/02. We went into the gift shop when we we got there to get towels. Since we were resort guests, the towels were free. They gave us a bunch and said if we needed more dry ones later, we could exchange them at Frostbite Freddy's I think, near the lockers. We never exchanged them.
I believe if you're not a resort guest, there will be a fee for the towels.