Is it appropriate to heat the device using CPU when it's cold? If I want the device to heat up for some reason (to warm my hands, to keep the display responsive below 0 centigrades, to avoid battery frost damage), is it appropriate to load all cores of CPU and let it heat up?

Can it damage the phone (or damage it more than the frost can)?
As long as you don't go full ham with your device's CPU load, everything should be fine in terms of damage/wear.  


  Remember that keeping your CPU active will grind your battery very quickly, but it might be worth, if you need your device's temperature to be above 0°C.