What are the low temperatures you're up against? Do you get a lot of sun still in the winter? There may be no magic solution if you get deep cold, but if the lows aren't too bad there are some tricks.
De-icers draw a lot of power compared to, say, a lightbulb or very periodic auto door motor. That makes solar quite expensive since you need a big panel and big battery, but there is also the issue of sun - you need a lot to keep the battery charged. Where I live, solar anything is pretty useless at times in the winter, and the tricks don't work in the coldest months. When it's 10F highs and -20F lows and I sometimes don't see the sun for a couple weeks at a time, all of my solar lights are guaranteed to go dead anyway. So...I eventually gave up and did extension cords onto a GFCI outlet. But, I did do things without electric for a while.
When I did things sans-electric, I used black rubber tubs which make good use of any sun that does hit them to warm up, but there's of course the same drawback of having to potentially refill 1-2 times daily when the temperature drops below a certain point. If the temperatures aren't too much below freezing, placing a rubber tub nestled in some composting substrate (which makes heat) and better yet where it can also get some sun if there is any might be all you need. Nestling a 1gal black bowl in composting substrate and giving it a bit of wind protection has worked for me into the low 20sF at night as long as there was sun in the morning to help thaw the surface ice. One downside: if you have any chickens with large wattles that haven't figured out how to lightly sip just over the edge of the bowl (I've got one such head-dunker rooster...), then they may have wattle frostbite issues with this strategy.