I'd be strongly inclined to take it with me if at all possible. Heat, moisture and cold are all hazards you can control if it is in your possession. In my last paid moved things were packed up on 2 different trucks, re-united and put into storage then moved to destination city - stored again and then delivered in a blinding rain storm. I stayed warm and dry as did my pets and machine and I always knew where they were. I've made seven moves in my adult life and five of them have been in horrid weather conditions. If it is important to you - keep it near you. If something does happened at least you know the what, where, when and why. One or both of your car and house insurance should cover it during the move.