The trip you are planning is terrific, doing it in a motorhome is not going to be fun. Any winter travel is suspect but not that different between a car and a RV. Many people panic at the talk of driving a RV in the winter because most of them never drive one anyway. If it were me I would eat the deposit and stay in motels and eat in restaurants, the cost is not going to be that much different (you will end up eating out most of the time anyway) and everyone will enjoy the trip more. If you were die-hard RVers, like many of us are, the inconveniences involved with winter travel are just be part and parcel of the RV life.
