Frank I did not want to comment to what you said above but what you said is killing me .If I had corrosion on any part of my starter circut I would have a problem all the time not just cold . The cold is not letting the current come through ,When a battery stays out in the cold its output decreases .The solar panel will just keep the electrons moving in the battery .
A quote from this web site
Solar Energy Devices
4. At our facility, we use the smaller solar panels on our passenger vehicles, placed on the dashboard under the windshield, inside the car. One of these vehicles is a very old 4-wheel drive pickup we use mostly for hauling firewood or snow-plowing the driveway in winter. Before we put on the solar panel (one of the smaller ones below) the battery would rarely have enough \\"oompf\\" to turn over the engine for more than a few seconds, especially in the cold wintertime. After putting a solar panel on the battery, which is an older battery at that, we have no more problems getting \\"old blue\\" started.
thanks Greg A.