Basically your options are something like this:
If you just want a llight source to work by (NOT to extend daylength for laying purposes), a $15 headlamp or a $40 solar shed light would do fine.
If you want light for daylength-extending purposes, set up a solar or deep-cycle-battery powered system, depending on the coop size (thus on what wattage you need) and how many hrs you want it to run and whether you want a timer on it or would settle for manual on/off you could be looking at $100-500, -ish.
To keep water from freezing, cheapest thing is to bring fresh water out several times a day. How often depends on your temperatures, but unless your temps are REALLY cold twice a day could easily be adequate. Putting it in a heavily-insulated vessel with only a drinking-sized opening (not a whole huge open bucket, for instance) will further delay freezing.
If you are experiencing super severe temps or cannot be sure you will always bring fresh water out enough, then the most obvious choice would be to use as low wattage a waterer heater as you possibly can and run it off a deep-cycle marine battery, either recharged in the house or charged off a solar panel with the appropriate accessories. Note that the better you insulate the waterer, the less watttage you gotta run and thus the longer a given battery charge will last.
Other setups are possible in principle, using ground-source or passive solar heat to keep a jacket warm under or around the waterer, but that gets pretty far into the realm of "I hope you like tinkering and have lotsa parts around and are not in a hurry to get it to work". Definitely worthwhile projects, but IMO more of an entertainment thing than a quick-fix practical measure.
Good luck, have fun,
Pat