I don't get the same problem as you - have a
big battery (and am not going to carry a spare around - far too heavy!) which doesn't stop functioning even on very cold NW European mornings
but it does start giving me warnings that my battery is about to run out of power (even a few hours after I've recharged the battery) - I've learned to live with the flashng red battery signs appearing on the screen bu it was very disconcerting at first!
Similar problem to that mentioned by
black in cold weather: when it rains (or, worse, drizzles or is misty) I tend to drop my camera under my hoody; of course, when I take it out it is very warm and condensation forms rapidly. I don't know how to avoid this - walk around with camera exposed and wipe off the mist or snowflakes before photographing (with resulting smears) or remember to wipe off the condensation (with resulting smears)? Or stay indoors in cold weather?