NOT solar powered. Battery powered that the solar charges the battery BIG difference
No not a big difference, in fact no real difference, batteries are simply a holding system they do not 'create' any additional power over what the solar input creates originally... The available energy in the battery can not exceed the solar input it gets unless you charge it by another means...
If one was to get these
http://www.harborfreight.com/45-watt-solar-panel-kit-10-pc-kit-68751.html that is a 45W solar panel, that means on the very best of very best days in perfect sun light, angled directly at the sun it might put out 45W of energy... Now there are additional losses along the way as well, you can probably subtract about another 20% in total losses between the 45W of potential energy taken in and the energy actually available to use after conversions...
Now as I said that is 45W/hour on the best of the best days and to optimize output it would require a tracker to move the panels and follow the sun (more cost)... But the reality is we don't get 'perfect' sunlight days and even if we do it's only for a few hours generally... If you look at a solar light calculator for your area you can estimate how many good daylight hour equivalents you get a day in your area
http://www.solardirect.com/pv/systems/gts/gts-sizing-sun-hours.html ... I live just outside Chicago, so during the winter months my solar daylight equivalent is about 1.47 hours... That means I could expect the above solar panel to put out potentially 45 watts for a whopping 1.47 hours during the winter, that means after additional losses it might be able to power a 40W light bulb for about an hour each day, that isn't going to heat your coop... If I wanted to power a 250W heat bulb for 24 hours during the winter, I would need approximately 100 - 125 of those panels! Or about a $18,000 - $22,000 investment...
If solar was cheap and easy everyone would be doing it, there is a reason not everyone is doing it...
ie solar powered electric fences are very limited BUT put the same fence on a big battery and have a solar panel that charges the battery and you get a fence with enough whallop to keep in a bull
World of difference...
Solar electric fences are very low wattage and they are generally pulsed... A good solar electric fence will only draw between 10 and 20 watts and have about a 100 microsecond pulse every second,to put that into perspective that means it's only really charging the wire for a grand total of 0.0864 seconds A DAY! They are designed to be efficient, heating devices are not...
You can go buy a 'stun gun' that runs off 2 AAA sized batteries and it will kick you to the ground and whallop a bull as well, doesn't mean those 2 AAA batteries are going to heat your coop...
FYI I'm an electronic design engineer by trade, pushing power numbers is what I do every day...