In my experience, some cameras handle cold better than others. If yours takes AA or AAAs, you may have better luck with the really expensive lithiums than you will with the alkaline.
Also, that camera-in-rice thing is neat. Rice draws the moisture out of electronics really well. Saved my phone after it took a dive into the dog water bowl. (and if you put the camera in a plastic bag in the rice, make sure the bag is open or it absolutely defeats the purpose).
