I think any frost based civ would probably need a building of some kind that generates ice boulders. There are actually some fairly interesting mechanics surrounding ice:
http://dwarffortresswiki.org/index.php/DF2014:Ice#Observations_on_constructing_with_iceBut generally, you can't easily produce large quantities of ice without being able to thaw and freeze on the surface. I suppose you could pump/haul water from below.
In terms of using ice to make things, constructions made of ice don't melt, but buildings, furniture and workshops made of ice do. Since temperature is an above ground/subterranean thing, ice buildings could be built inside surface structures made of ice as long as it never thaws.
This civ would probably also need a building that converts ice boulders into drinkable water, since ice boulders can't be melted into drinkable water. It would be interesting to set up, because you'd have to have the input side of the building be above ground, and the output not just be inside, but subterranean.
It might be that DF's handle on temperature just isn't sophisticated enough yet to make this concept worth while.