2019-01-14 12:47:08.959 Meteorologist[295:2925] <error>: Invalid Weather Code : weatherDataSource=0, weatherCode=</error>
Ok, that makes sense. We've had several straight days of haze and mist, so it's probably been trying to use just that one icon the whole time.
I switched to DarkSky due to Y! going down. It's fetching the data properly but I'm now getting exactly the OP's problem of the icons not showing up (only a question mark). Meteorologist 3.1.4, MacOS 10.14.2. Any thoughts?