Glaciers, schmaciers

It appears that Himalayan Glaciers are rapidly replacing polar bears as the Warmenists' poster boys (objects?). For example, Richard North points out that not only does Mr Pachauri have a personal financial interest in the carbon permits scheme, he also has a personal financial interest in us stumping up for more research into said glaciers*

The Warmenist line appears to be that if the glaciers melt a) it will cause terrible flooding and b) once they are gone, the rivers they fed will dry up.

OK, I'm no expert in glaciers, but the way I understand it is this:
1. Rain or snow lands on glaciers high up the mountains.
2. Glaciers slide down the mountains and melt a bit.
3. The same rainwater or melted snow pours into the river, and is used for drinking water, irrigation etc.

In warmer countries, the model seems to be:
1. Rain or snow falls up in the mountains or hills.
2. Streams flow down into rivers.
3. The rivers carry the same rainwater or melted snow, which are used for drinking water, irrigation etc.

So the fact it is bloody freezing up in the Himalayas etc slows down the time it takes for water to get from top to bottom, but the quantity of water flowing down the river into the sea must, ultimately, be much the same as the quantity of water falling as snow or rain up in the mountains or hills.

Or have I missed something?

* In fact, Mr Pachauri seems to be to Richard North what Richard Murphy is to Tim Worstall, but that's another topic.