Freezing Mechanics: Water freezes below 10000 U.
what this means in practice is that tiles with the light, outside, and above-ground flags in cold or seasonally cold biomes will freeze. there are no known methods of inducing freezing(?) beyond weather.
temperature transfer using items or other methods is on the list of future research.
specifically of note, nether-caps have the tag [MAT_FIXED_TEMP:10000], meaning they are stuck at freezing temperature, but if I recall, this can never bring the water below 10000, and thus can't induce freezing.
Freezing Methods: Ice farms in seasonal biomes where the temperature fluctuates above and below freezing are as simple as channeling out a square and flooding it. due to the mechanism of freezing, a column of water will freeze as readily as a single tile deep pool. (tested only on a freezing biome) so a channeled cube should freeze as readily as a channeled square, making this method as salable as necessary
Freezing biomes that never rise above 10000 U can be farmed as well - exploiting the subterranean tiles' constant 10015 U temperature, a grid can be made of underground tiles to allow water to flow freely, and above-ground tiles that freeze water that spills onto them.
https://imgur.com/a/6V9a53Wblue pixels represent below-ground water tiles, white pixels represent above-ground freezing tiles.
the first pattern has an efficiency of two ice tiles per flooding tile, while the second has a much better 4 ice tiles per flood tile.
using a floodgate or bridge, water will spread freely through the farm while simultaneously creating 4/5ths of the total farm area of ice. by restricting water flow and draining excess, the farm can then be mined out, the ice hauled, and the farm reset.
due to the difficulty of finding liquid water in a freezing biome, the most efficient sources of water are going to be a partial-map aquifers or adjacent oceans.
Ice farm in freezing biome using an aquifer (
https://imgur.com/a/VzHhUov) for safety, the freezing level is designated restricted,and the level above is high traffic.
Alternative methods of creating ice include creating a pond zone and allowing dwarves to manually fill it; two bucket trips are needed for a full ice wall.
liquid transport using minecarts is possible, however, seems much less efficient than buckets in terms of setup
Using Ice: Water freezing instantly kills units trapped within it:
That sounds alluring, but given how difficult controlling temperature is, becomes impractical. The easiest-to-create freezing trap is likely a two tile wide channel with subterranean fortifications on its sides. the fortifications would prevent creature movement out of the freeze tiles while allowing water to move in. managing water flow such that the entrance and exit of the freezing corridor freeze first, insuring anything caught can't escape would be the most efficient. remember that a tile needs only to be exposed to the sky once to be considered above-ground, and floors or walls can be rebuilt above it to preserve security.
Notably, if ice is created on top of a cage containing creatures and the cage is released with a lever the creatures don't die. furthermore, if the ice has any free adjacent tiles the creatures will move to them as if the ice were not there at all. this is likely a facet of caged creatures being semi-invulnerable (to drowning and to magma, among others)
Ice walls frozen from water can be treated as stone, including being smoothed, carved into fortifications, and engraved, with the caveat that if the temperature rises above freezing natural ice will melt. This applies to ice boulders mined from ice wall as well. they can be used for nearly anything a rock can with some exceptions (ice cannot be made into mechanisms, statues, or anything that requires a non-economic hard rock, for example)
Constructed structures like walls, floors, and fortifications built with ice will not melt (and can contain magma)
Theoretically, the delineation is items from the b-C menu won't melt, but everything else including bridges and workshops will. If anyone is seriously interested in exactly what will and won't melt, experimentation could be done for all uses or specific uses of ice by request.