Power is going to be your biggest problem, because just an Arduino on its own will use enough power to require quite a substantial solar panel by the time you allow for night time and poor weather conditions and so on. Adding in what sounds like a very substantial power demand from a motor will make the problem much harder - depending how often you need this motor to operate, and where the device will be located, you could be looking at yards of solar panel. On the other hand a deep cycle lead acid battery that you took away and recharged every few weeks would probably be feasible.
A stepper motor is not very efficient and requires power to hold itself in position. You would probably be better off using a geared DC motor, with an encoder to measure how much line has been wound, or some form of limit switch activated by the line.