Many of the cabins on Lake Vermilion, where I live, did not have electric power available until around 1950.  Most had their own ice houses; which now are turned into storage sheds.
I helped put up ice when I was young.  Ours would last into August and we used it in old fashioned ice boxes.  We would dig a block out of the sawdust, take it to the lake and dunk it to clean it off, then to cabin and into ice box.
I think the sawdust idea for packing food sounds like a good one.
Now I freeze water in several 1 liter pop bottles and use them for the ice packs in my cooler.  As they melt you can enjoy the fresh and COLD water for 2-3 days on the trip.  Then I use them to store filtered water at camp and on the trail.  One of our party is put to work filling them with filtered water in the morning, and then it is handy all day while traveling.