This is driving me crazy because I see this in notification center in a lot of a screenshots for iOS reviews:
What is the app that adds weather to the notification center?
It's not available on iPad. It's an iPhone feature.
To get the same on the iPad, you'll need to jailbreak it and download an app called "Stock NC Widgets for iPad".
It doesn't appear to be working yet, but its what you are looking for.
It's in your Settings -> Notifications -> Weather Widget.
You need to jailbreak your ipad (use evasi0n) then load the app onto your iPad.
Follow the instructions here: http://www.sinfuliphone.com/showthread.php?p=953237
On iPad mini this worked fine, but iPad 3 it works with the caveat that the images for the multi-day forecast don't show.