Ice free water

Can I ask a couple of questions first?  First, how much water is in the trough and what's the lowest temperature you want to have ice-free water available?  What temperature do you want to try to keep the water at?  (Just thinking 33º might be a little too cold to drink.)  Assuming you want to keep water available for a number of cloudy days, you'll need batteries, so how many days to you want to guarantee icefree water?  More days = more batteries.

John, I'm wondering first, why you think its expensive and secondly, why you think its more expensive than installing and maintaining a piped supply to and a pump itself in freezing conditions.  If you did go that route, then you still have to power the pump, so solar panels (and batteries) would still be needed.  A simple panel (and maybe batteries) connected to a small resistance heating element (maybe more like heat tracing) might be just the right solution.  Certainly much simpler. If the temperature difference isn't much and there is some insulation available, power reqirements could be quite small.