I’ve installed Office 2013 a few days ago and tonight when opening the calendar I saw a nifty feature at the top showing the current weather forecast (including 2 days in the future) with the minimum and maximum expected temperatures.
I needed to change the location and temperature unit as the default was for New York and the temperature unit in Fahrenheit. To be honest I would have thought that Outlook should be able to pick a default city for my time zone but it’s not a big deal.
Below is a short video on how to change this if you are running Outlook 2013. (View the video in 1080p for best experience)
Exchange Times 
July 5th, 2013 at 10:16
This was helpful, though my version is different – I had to go in to the options under the ‘cog wheel’ icon beside my name, top right of the screen. Still, you gave me the idea as to what to look for, and that the change was possible – I now see the weather for the South of France, where I am, not for London!
July 5th, 2013 at 11:43
Glad the post sent you in the right location. Interesting that the versions are so different.