You certainly can run a light off a battery (for heat or light) and you can charge a battery with a solar panel. You will need to figure out how many watts you need and then size your panel according to your sun exposure. I'm betting it probably wont fall into most people's definition of small. Also, you may need more than one deep cycle battery depending on load. One suggestion... If you only want heat, use something that only puts out heat. They would be more efficient. If you go the solar route, it will probably be expensive too. Also, you will have to clear snow off the panel.