Arguably some people might think the what version is more appropriate when the speaker is specifically interested in knowing what the weather actually is (or perhaps will be, later in the day). Conversely, the how version might be more likely if what the speaker wants to know is how the addressee feels about the weather. Source: https://ell.stackexchange.com/questions/174118/what-is-the-weather-today-or-how-is-the-weather-today.
