The way it works is that dead pixels tend to be strongly correlated with Time value (exposure duration) and Temperature. The longer the exposure and the greater the temperature, the more dead pixels there are. Temperature doesn't usually become a factor in until the exposure gets longer than 1/5 second or so. Canon doesn't let you adjust the time value of their dead pixel remapper, but at least you can control the temperature.
I don't think it can cause damage. At least, I've never heard of it being a problem. The cold weather does reduce thermal noise ("dark current") though, so it is definitely helpful for those 10 to 50 minute exposures. An alternative method is to just take many short frames and add all the frames together in the computer.