We freeze 2 liter bottles and fill the cooler before we leave. The frozen bottles will last for a couple of days, if we shoot something, we then buy bagged ice. The cooler is already cold from the bottles of ice, so our ice lasts longer.
Our other option is sometimes we haul a small chest freezer when we have access to electricity. I bought it used for a $100 and have hauled it all over the country. Loaded with frozen 2 liter bottles, it will last for a day without power. Just don't drive off with it plugged in.