under such cold and minus weather conditions, it is more likely the camera itself (understand it mechanics) which will lead to problems: mechanical parts of a camera are "greased" with special lubrificants. These lubrificants have a tendancy to become thicker and less fluid, thus affecting the movements and sometimes blocking it.
At Sinar we have some special lubrificants, especially for people working well below 20°C (most of the lubrificants will become thicker below 20°C), on request and for our view camerras and other items with mechanically moving parts. Those lubrificants can also be found elsewhere.
Also, and as said by all, the batteries are much affected under cold conditions: try to keep them warm all the time. Have a set of batteries with you which you change on regular intervals, about every 10 minutes or so. Keep the spare ones warm.
The digital backs will certainly not stop working, even under extrem cold conditions. One thing you will notice, is that noise is almost no issue here: the cooler the better for the noise level.