It's easy. There are three ways to do it.

One is to put a NOAA band reciever into the phone. That would make it bulkier and cut into battery life, but not radically so. But I haven't seen a cell with FM capabilities yet, and weather band is much more of a niche market.

The next is something called "reverse 911". Everyone in a given area is called by a computer pretty much simultaniously. Places near nuclear power plants or where there are tornados have been talking about it for a while, but I don't know of any wide spread implimentations.

The easiest way is to sign up service that will alert you. I think the Weather Channel has one for text messages.

The problem with the latter two is that cells roam. Conceptually, it wouldn't be too hard to get an idea of where you are by what tower(s) you are contacting, but that would create an amazing amount of overhead. None of the cell providers woudl do it, no profit in it.