perhaps you could get the water boulder to turn into ice boulder by water-filling the cart on warmer temp area and then carrying it to colder area?
Apparently no.
I expected it would eventually melt, but it decided to disappear instead..... it also certainly doesn't show up as building material, nor does being flung against a wall get one an ice wall like one would expect with 2/7 water freezing....
However, it does get dwarves to clean the beach of water occasionally.
Still, I'd expect any biome cold enough for ice to remain year long is too cold to live outside year long, and it seems like it'd be exceedingly difficult to make ice-walled living areas even warmer to colder biome without losing access to the depot - perhaps using ocean waves over a ledge where downstairs are built, netting potentially 6 wide living area with two-material 7 long bridges for place to wash across, or dropping items in volcano to get magma mist erasing ice (object testing arena suggesting that ice gets converted to steam without becoming water in-between).
Of course, if you can get ocean waves brushing over a freezing volcano it seems like you might be able to have dwarves warmed by it's obsidian floors while surrounded by ice walls (depending on how the drop works out on vaporizing versus freezing) with access to water in a small hole. Though it seems like only 1 z-level drop could perhaps be traversible while maintaining trade, given that typically built ramps are removed from same z-level as they are.