Assuming it is colder outside than in your inner pocket, and assuming your inner pocket has air that has high relative humidity, you could get condensation on the camera by taking it from cold outside to semi-warm semi-moist inner pocket. Do it a few times and the worst that would likely happen is a foggy lens, but more often could result in some excess moisture getting into the innards. It might be a hassle, but putting the camera in a plastic bag and then putting that in your inner pocket could keep the condensation outside of the plastic, protecting the camera. It would not have to be air tight or water tight, just enough to reduce air flow. Assuming it is a small point and shoot, even a sandwich sized bag should suffice.

I quite frankly do not know what the best cold weather batteries are. Perhaps Lithium (the disposable, not rechargeable) batteries? You might want to do some internet searches.

I have seen some cameras stop working on disposable batteries but my GPS battery level indicator said that the batteries still had 80 percent life left in them. I think the rapid drain to charge the flash capacitor was the issue.
So, you might want to manually disable the flash if your camera has such a setting. I always leave the flash disabled on my cameras when I travel unless I specifically want it on for evening shots.