The cold temperature isn't an issue, chickens are fine below 0. Remember that folks in Canada and Alaska have chickens too. The lack of liquid water can be a problem - either you need to keep bringing out liquid water throughout the day, or invest in some form of heated waterer.
Do NOT be tempted to close up the coop and run to keep them warm. Ventilation is key, you need to let moisture escape so they stay dry. Dry chickens are warm chickens.
The smallest coop (assuming you haven't altered it), is underventilated, by the way. If the door and window cannot be left open/propped open, that would be the one I'd be most concerned about.
If winds are an issue you may want to buffer the run walls facing oncoming winds with clear plastic.
This say's it all @moisture , ventilation is the most important thing, more important than stopping drafts IMHO.