Lets Talk About... the Weather
A common piece of writing advice is to *never* start with the weather. Many say that, "it's not interesting and there are better ways to set the emotional tone of the story."
Here's the thing, like most writing rules this is just a guideline. And as is often the case, it's really indicating that there is a related writing tool that you can learn to use.
So, what's the right way to write about the weather?
1) Make it relevant to your characters actions.
Your main character opens the door and sees that it's snowing, she turns to grab her hat with the door still open, then a robber runs in and holds her at gunpoint. This is a great use of weather, it's affecting the main characters actions, which in turn affect the plot.
2) Make it relevant to your characters relationships.
Your main character and their romantic interest are walking down the street and it starts to rain. They rush under the nearest shelter, which happens to be a small shop overhang. There isn't much space so they have to stand close together. They aren't thinking about the weather though, they're thinking about the situation it caused and how they both feel about the other person. This is a great use of weather to bring the next step in a relationship out in the open.
3) Don't let it distract from the main event.
A lot of the reason that this advice has come up in the first place is because the weather was used to set the tone, or add to the tension. Yet the weather feels like such a small thing to the reader when the main character is in the middle of a chase scene that it's distracting. The weather should affect things from the background, without taking any of the spotlight away from the main plot.
If you don't want to use this tool then continue to not start the story with weather and you'll be safe. On the other hand you can use the weather to your advantage to strengthen the tension in your book and make the plot shine.