The BBC and ITV have a system, which is a bit ad hoc, to cope with missing kids don't they?
In terms of things like school closings, that's definitely the province of BBC Local Radio - and everyone knows to tune to it if there is bad weather, and the Breakfast News regional bulletins will include a "For full details of school closures because of the bad weather, check with your BBC Local Radio station".
One thing we could take from US 'local' TV is scrolling captions on network output.
There's no technical reason why the regional BBC centres couldn't have an info ticker on the screen during Breakfast, (and any other time during local emergencies). Rather more difficult for ITV, because of their different network architecture, (they'd have to install gfx engines at Chiswick and Leeds on each regional Tx feed)