I had been wondering the same thing. The trouble is, calibre didn't take any of my rss weather feeds. All I got was an error message. I finally found a way. BBC weather seems to work:
http://www.bbc.co.uk/weather/.
Go there, find the location you want and then click on the rss icon under the forecast. A menu comes up, select next three days. The feed will appear. Make sure you're using IE or something similar so that the URL of the feed shows up. Then, in calibre, create a custom news source, add the URL of the rss feed and set the advanced settings to this:
Code:
class AdvancedUserRecipe1367658633(BasicNewsRecipe):
title = u'Weather'
oldest_article = 1
max_articles_per_feed = 1
auto_cleanup = True
feeds = Your feed URL here...
Now all you have to do is save and download.
A bit messy towards the end, but it works for me.