As long as there is ice in the water inside the ice chest, you should not drain it unless the contents are being damaged by the water. When water still has ice in it, the water is at or near 32 degrees F. If that is colder than the air outside the ice box it is continuing to cool the contents. You should not drain it unless you the contents are being damaged by the water. A good solution is to put your ice inside a “Dry Bag” like is used for kayaking to keep things dry. As the ice melts, the water will stay inside the dry bag and not damage the ice chest contents. Keep in mind that when you drain the water, its volume is replaced by warm outside air. Thus warming the ice chest contents.