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.
ninny my dad use to add a few drops of glisten to the water for the ducks and rabbits that we had.
You can also go to one of the big box stores and get some heat tape. Its an electrical wire that draws very little energy and you can wrap it around the water supply.
A heater for the chicken fountain I have cost me $50 but it requres a 110 volt source. PatandChickens gave you some good suggestions. The heat tapes are now thermostatically controlled to come on at 38F...which it gets here in summer. We get -30 F on a regular basis in the winter from late DEC to early March.
Insulation, heat tape and reduced size of the exposure to the hole where the chickens drink will all help. Styrofoam works well for insulation. You can buy it in 2" sheets 4 x 8 feet for about $25/sheet and make your own design. (I've done that too!)
An incandescent light bulb will definitely generate enough heat since they are 90% heat and 10% light...but the slightest drop of water on them and they will shatter...exposing the conductors/filament which is not conducive to health and long life of chickens. (Don't ask me how I know this...) I did find an article in Farm Show magazine where a guy used a concrete block to hold the light bulb and he felt that it worked very well. I did try that and while the heat generated is plenty, the exposed glass bulb would get the slightest drop of water from the fountain and blow up...not fun!