You have to remember that surface area increases with the SQUARE of size, but volume by the CUBE. So scale it up by a factor of 10 and you have 100x the surface and 1000x the volume, so it will melt much slower.
Scale it up by ANOTHER factor of 10, and it'll melt another factor of 10 slower, and possibly more. Building-size blocks of ice take months to melt, even in warm temps.
It applies regardless of scale. The proposal had internal refrigeration, and air is a very poor conductor of heat - most of the heat transfer would occur with the water, not the air, even if the air was 10-20 degrees warmer, maybe more.
Scale it up by ANOTHER factor of 10, and it'll melt another factor of 10 slower, and possibly more. Building-size blocks of ice take months to melt, even in warm temps.