The Canon specification is the same for both - 32-104°F/0-40°C (actually, it's the same for the 1-series, too).
Speaking from personal experience (New England winters), the camera does fine in sub-freezing temperatures. The first thing you'll notice is the reduced battery life you already mentioned, also the LCDs will stop functioning in extreme cold (including the transmissive LCD, although Chuck Westfall mentioned that the 1D X's transmissive LCD is built to withstand much colder temperatures than the 7D).
The bigger issue isn't functioning in cold temps, it's what happens when you bring the camera back inside and the cold results in condensation forming inside camera and lens. Here are some tips on that.
Fast and dramatic changes in temperature are very hard on mechanical and electronic things. Throw in humidity and its worse.
Just considering the mechanical issues, which is 99+ % of the problem ...
Almost all parts shrink in cold weather and expand when hot. However, different materials expand and contract at different rates, and composites can be weird since they may have components that shrink and others that expand.
The net result is internal stress which is accounted for in the design (hopefully). Exceeding the design temperatures, hot or cold, can cause metal fatigue it it happens frequently, or the stress will loosen or damage (crack) joints, etc.
There is a safety margin, but heat and cold do take their toll.