The only thing that doesn't like cold is the battery, so it may be wise to keep the battery in warm pocket. (I think it
should still work up to -10°C.)
The image sensor will actually have less noise at lower temperature.
Bringing the camera from a warm room into the cold: I think the biggest worry is the humidity of the air in the camera condensing in the surfaces. That only happened to me with my old camera after using it in the rain or submerging it in
water (don't ask).
You can keep your camera in a camera bag with desiccant for a few days… or just hope it doesn't condense on the glasses. The sensor will heat up during use, so this isn't an issue.
About bringing it from cold to warm: The humidity of the room air may condense on the camera. Mine is supposedly rain proof, so I don't care about that. The lens will be fogged up until it warms up.
Over all I don't expect any damage.