Everybody has a different way of winterizing marine electronics. If you look on the manufacturers page they may give you a guide line on what should be done but I will summarize it here. When your getting ready to store your boat there are a couple of things that need to be done to make sure everything will be working properly in the spring. First make sure everything turns on and is working properly. After that you should take down the model numbers so you can check for updates. You should pull all the connections and make sure they are clean and put some di-electric grease on the pins. Lastly put the covers over the screen after cleaning them. If the electronics are easily removable and you are worried about someone stealing them I would take them out of the boat. On the other side of it, all of these electronics are tested to be in severe cold weather and as long as your not boating in the arctic circle the cold should not affect them at all. This being said if your electronics are flush mounted I would not go through the hassle of removing them just because you do not want them out in the cold.
Chris
DIESEL SMITH L.L.C. 