We took Ziploc freezer bags with us. Each day the room steward would bring us fresh ice; we'd fill up a freezer bag and put it in the cooler. We were able to keep water bottles, wine, beer, sodas, and juice bags quite cold.
Each time we took something out, like a water bottle, we'd replace it with a 'warm' one from our supply in the cabinet ... nobody ever went without a nice, cold drink!