Just wanted to report that I also have this issue after upgrading to iOS 6 on an iPhone 4.  One night at 11 pm my phone used 600 MB of data - triple overage - while I was sleeping.  I am on the lowest 200 MB plan since I am on wifi 98% of the time.  Rarely have ever gone over limit before.  Chatted online with AT&T - told me at first it was my issue - but eventually gave me credit for the overages.  I am happy with AT&T but not with Apple on this.  

I was also in a meeting yesterday and everyone with an iPhone that had upgraded to iOS 6 was dealing with the exact same issue.  I am surprised this has not blown up into a larger story yet.