Hello,
I am a solar energy engineer and I don't believe this is practical IF you are talking about using solar ELECTRICITY as opposed to heating air, water or some other substance with the sun's heat directly.
Here's some math that explains why I think the solar electric approach isn't practical:
Say you want even a meager 100W heater for 8 hours overnight.  You would need 8*100 = 800 Wh of energy.
Say you get 3 sun hours per day in the winter- this is location and climate dependent.  (I got this number from here: 
http://rredc.nrel.gov/solar/pubs/redbook/).  Say you have a meager 200W solar panel, this would be about 3'x5' and cost about $800-$1000.  This would give 600Wh (200W * 3 sun hours) of energy and you'd lose maybe 20% of this by storing the energy in a battery during the day when the sun shines, and then taking it out of a battery at night. This leaves 480 Wh of energy - not enough for your meager 800Wh that you need to power a 100W heater for 8 hours.  You'd need 2x as much solar capacity at least.  That's maybe $1600 to $2000 just for the solar panels alone.    I don't have expertise with batteries and charge controllers so don't know how much they'd cost, but I'd budget maybe $500 for those as a guess.  And this is only for a 100W heater which is barely enough for a small coop.
Disclaimer - the 20% battery loss could be overly optimistic so if anyone plans on doing this you should check this with a battery expert - I know a little about them but it is not my expertise.
Another disclaimer - the 3 sun hour assumption in winter is a reasonable AVERAGE minimum, however with solar/batter systems, if you want to be absolutely sure you don't run the battery too low during a period of very low sun, most would assume that you might need to go 3 days with NO sun at all (3 crappy cloudy days in a row).  In this case you'd size your batteries 3x larger than you would need for one night.  This would be 3x the cost for the battery portion.  Sorry I don't have cost numbers for that, but for one day you'd need about a 12V, 100 Amp-hour batter and for 3 days you'd need a 12V, 300 Amp-hour battery (these are rough estimates).  Car batteries should not be used, but deep cycle, golf cart type batteries.  You can get them at marine and RV supply stores.
Bottom line:  run an extension cord, and/or consider a passive solar design with well placed windows, eaves, and insulate well. Or, maybe you can find someone more clever than I who has figured out how to do this!
If anyone wants to follow up with me directly with questions, feel free!
Colleen