Hi Aaron,
My name is Ardiane, a Guru here at Shopify!
That sounds like a great idea for a widget to have in a store! Unfortunately, we haven't developed anything like that nor have any apps that would display live opening hours or that amazing idea regarding the change of opening and closing times due to bad weather.
I can definitely send it up to our Feature Request team to review for an app or a widget in the future but there wouldn't be guarantee with it as it would really depends on how necessary it is for our merchants. However, I wouldn't hold you back if you'd like to have a look at our Experts page to find and hire an expert that would build this for you! It really does sound like a very interesting thought but at the moment, we don't have anything like it.
I hope that helps you out!
- Ardiane :)