> It gives a temperature reading for any pixel I select, but appears to be interpolating from a relatively limited number of real-world data points.
I think you are misinterpreting what Windy is showing. It's not trying to show the current temperature at the selected location, it's showing the current forecast for the temperature at that location according to a particular model. On the lower right, you can choose from different forecast models, and the "temperature" at the location you select will probably change. If you choose a finer grained model than the default (there are different third party models available for different locales) you might find one that does a better job of dealing with mountains. And on the lower left, you can change the "time" slider to show the forecast for the next few days according to the chosen model.
So yes, there is interpolation happening, but it's interpolation from a model that is already based on an artificial grid, and not based on interpolating from the actual temperatures as recorded on the ground. What I find useful about Windy is the ability to compare the output of different weather models, and thus get a idea of the uncertainty of the forecast. To access this, choose a location, and then click "Compare" on the bottom bar. If all 5 models available to me agree, it's probably a good guess. If one of them is radically different, one should be slightly skeptical. If they all disagree, probably best to assume that the forecast is inherently unpredictable.