Light are easy. Crappy ebay 12V LED bulbs should give a decent service life for anybody crazy enough to ice fish. Stepper motor windmill (or VW solar panel) would keep the battery charged for most people. Depends on how much the light is used.
"Small" is relative. 100W is not exactly small.
The heat output of 100W is 340BTUs/hour.
I recall reading a human makes 350BTUs/hour at rest. If that is correct, then the windmill needs to make about 100W to heat the shack as much as your own body heat.
Paint it black outside, white inside, insulate it, and a Mr Heater (whatever it is).
G-