Can the potatoes be boiled and then cooled or chilled and finished off later at the camp site? Be sure to add lemon juice concentrate to the water, after boiling and before draining to keep the potato from darkening.  If so, storage could be in a small cooler or insulated bag such as they use for delivering pizzas. These bags can be found at camping stores like Cabela's. I would add ice to a cooler to get the interior chilled, then dump out and add in the frozen blue ice style containers before heading out on the trip. This can often extend the holding of the potatoes to a day ahead. Place the potatoes in clear zipable bags, pressing air out and refrigerate (or, if cooked, these can be frozen so they partially thaw when on the trip.)