Hello,
I think I figured this out from the above instruction. I also have Windows 10. So follow the above from Settings to Lock screen. While on Lock screen go to: Choose one app to show detailed status on the lock screen. There you should see your weather update icon that is causing this problem. Click on that and you see options to choose other icons. Well, at the very top of those selections you will see None. Clicking on that means you choose no icon. And that should do it. Good luck..