How cold is to cold to build in and not be worried about strength of adheasive or any other issues???
I would keep adheasive in a warm area untill needed.
and replace when done.

I use pro Bond White glue and I build in any temperature I can stand. It is extremely strong, set's fast and dries overnight. Whatever you feel comfortable temperature wise go ahead and build. If you're unsure of the adhesive you're building with, just glue two like scrap pieces of wood together and test them for bond. Bob Laine

I'd be worried about 32ºF for anything with water in it, probably white/yellow glues. Epoxy may not "kick" well if too cold, but I've used it down to 45ºF or so on boats in the Spring. Most adhesives have a suggested range if you contact the manufacturer. Most paints warn of temperature minimum, 50ºF or so for flow and adhesion.

If you're doing something like taking the CA and parts outdoors to glue (both being warm to begin with) I wouldn't worry at all. But if the parts are in an unheated area and you're bringing the adhesives out I have no idea what CA's temperature tolerance is.