Hi,
I've no experience with Davis stations so can't say if it would be possible to put a heater inside their sensor. It would be
really easy to do with a Fine Offset sensor, but the fact that nobody seems to have reported success (or even tried? ) might be a clue.
The "heater" should be easy enough, just use a "watty" (usually wire-wound) resistor of a value to suit the available supply voltage. Alternatively, an "old school" incandescent (e.g. tungsten filiament) lamp, somewhat under-run on voltage can make an excellent heater.
The real issues are "How much heater power is required", "Where does the power come from" and "What controls it"? Melting ice needs
lots of power so you probably need a wired system to a mains power supply (which might solve the other issues). But a thermostat would be wise if it can't be switched off manually (and you have the expertise).
Personally I wouldn't even consider "solar" powering, because of the probable unavailability of sufficent power when it's needed. But if you want to look at the possibilities, I suggest the
WeatherDuino forum. Because it uses "off the shelf" Arduino controllers, it has far higher remote (external) power requirements than a "normal" station. However, its 1 watt (12v, 100 mA) supply is probably still much less than you'd need.
Cheers, Alan.