Yeah. Having a camera out in the cold and then immediately taking it indoors is really bad for the gear. What I do sometimes is take my bag out with me, so that it cools down. When I put my camera back in the bag, the bag isn't hot/warm. My camera bag will actually stay pretty cold for a while and even when brought indoors, my camera is still cold for a good hour or so in the bag. Another method I've heard is to wrap the camera in a plastic bag before taking it indoors. Another is to immediately put your camera bag in the freezer and then gradually warm it back up.
As for getting sticky, i don't notice it. It's more my numb fingers
