When asking questions about weather, do you use how or what?

You can use how/what to ask about the weather.

When How is used to ask about the weather, the structure of How’s the weather? is often used.

When What is used to ask about the weather, the structure of What’s the weather like? is often used. Extended information

How asks how the weather is, such as good or bad. Using how means how hot or cold the weather is, mainly describing the degree. It means that you already know whether the weather is cold or hot, so you can only express your feelings about the heat or cold.

　What is used to ask about the weather, such as sunny, rainy or cloudy, and using what means asking what the weather is like, whether it is cold or hot, and you don’t know at all.

For example, what's the weather like in Shanghai, what's the weather like in Shanghai? It means I don’t know whether it’s cold or hot. Want to know by asking.