During this time of the year the outside weather can drop well below 30 degree (Northern California) making it very uncomfortable for you and your equipment.
Common practice for cold weather photography is it to get the camera body and lenses as close to the ambient temperature as possible and as gradually as possible.
Also during this time of the year I place a couple of Desiccant (Silica Gel) Dehumidifier packets in my camera bag. They are cheap and easy to get, and I highly recommend them.
When I photograph and outdoor event where the temperatures are below 40 degrees I will place my camera and lenses in my camera bag about 2-3 hours before the event and place it in the trunk of my car. This will allow the camera and lenses to slowly drop to the outside ambient temperature. By allowing your camera and lenses to slowly chill down you minimize the chance of moisture forming on the lens and or the camera when you take them into the cold. A fogged lens or sensor will cause some pretty interesting effects, mostly unwanted effects.
Now having said that, I am not suggesting that you do this unless you are comfortable with leaving you camera somewhat unprotected. I don’t want to give you advice that may get your equipment stolen. Please be careful.
The gotcha on this is that batteries don’t like the cold, so keep a spare set of batteries in your jacket pocket or in your camera bag along with a silica packet and swap them out as needed.
Also, something as simple as breathe on your camera you risk fogging it as well and placing your warm eye to the viewfinder can fog the viewfinder glass, so just be aware when you are in the cold.
After I am done shooting in the cold I will place my camera back into the bag and zip it up then take it into the house and let it set for a couple of hours to slowly let it come back up to room temperature.
If you know that you will be moving from cold to warm places rapidly (like going outside in to the cold from a warm house and or vice versa) I recommend that you keep the camera in a camera bag with a couple Desiccant (Silica Gel) Dehumidifier packets when you are not using it. The silica packets will absorb any moisture that may start to form due to rapidly changing temperatures
It is not a good idea to place your camera in your coat as this will introduce moisture and could raise the temperature of the camera and lens enough to fog them up and create condensation. Your camera is better off cold and dry.
I do wear gloves when I am shooting in the cold. I like to use us a pair of framers glove when in moderately cold weather. With framers gloves the tip of the thumb and the first two fingers are cut off at the first knuckle allowing direct contact with the camera and its buttons. When it gets really cold I use a thicker pair of gloves that have a thin liner so that when I am ready to shoot I remove the outer shell glove but my hands and fingers are still protected.
Have fun and stay warm and dry