We have icehouses on Ara, Meta and Stone Lake. We work very hard to cut ice out of the lakes in the winter. We cut them into blocks, put them in the icehouses and then cover the ice with saw dust and wood shavings.
If guests only use what they need and make sure they re-cover the ice with the insulating sawdust after they have grabbed a block, there should be ice in the icehouse for the whole summer. Failure to re-cover the ice with sawdust means the ice will melt very quickly.
With this in mind, you do not need to bring coolers full of ice on your trip. Just bring enough to keep your food cool for the flight in. When you grab a block of ice from the ice shed, you only need to dip it in the water to clean it off and you have fresh crystal clean ice for drinks or coolers.