Hi E36is, you raise a good point!
What coverage you purchase should depend on the value of the beater. If you can afford to replace the car if it is a write it off, then carrying only liability would be fine (and the cheapest). Otherwise, go with full coverage.
With respect to switching cars up if the need arises; you don't need to leave comprehensive on the summer vehicle to do that. However, If your summer car is older, to re-add it; your company may ask for pictures, an appraisal, or a safety certificate if you didn't leave comprehensive on it for the laid up months. They may not even allow you to add it back on. The rules for a car currently listed on a policy vs. a car that has to be newly or re-listed can be different.
When calling your agent/broker to make arrangements for your winter beater, discuss the process of re-adding your summer car to make sure you aren't creating future headaches.
Point of interest: Comprehensive coverage is not affected by your driving record. If you have a recent at fault accident or have never had one, the rate your company would charge (exclusively for comp.) is identical.