So all you need to do to have the automatically updated weather icon is manually update the weather icon when you want it automatically updated?

Incredible!

But you have to open the page to update its icon, right?

It's not really "auto-update" to me.

Awesome idea. iOS only, I presume?

For weather at least there is no need for this on android. Just use the google news & weather widget.. or a widget for any task you want updating icons for that matter.