Pam came up with a great solution. Here's how I did mine, based on her idea. Here's what you need to purchase: unscented Huggies wipes (I bought the heavy duty ones); Ziploc sandwich bags; and Florida water, which can be purchased at most drug stores and probably at many sporting goods stores under various brand names.
I mixed one cup of water with a teaspoon of Florida water. Place one wipe in a sandwich bag and pour in about 1/8 cup of the water mixture. Seal the bag, getting the excess air out of it. This mixture did nine bags. Place the bags in the freezer. When you leave for the golf course, place the bags in your ice chest.As you need to cool off, remove one bag and use the disposable wipe to wipe your face and neck. Ahhhh. How refreshing! And now you can share your "coolness" with your cart buddy. Thanks, Pam.