Hi Don and wife.
We're having the same issue.
My husband and I got iPhone5's on Friday night. He did pretty much nothing with his, while I set up my Yahoo mail, facebook, twitter, instagram, the Walgreen's app and the Weather Channel app (they should package these together as an Old People's Suite) and turned on iCloud.
While connected to my wifi, the phone used 425MB of data, nearly all showed up as 'received' data.
I have read that the phone drops wifi when it goes to sleep, so it's reasonable to believe some of this happened overnight. I have also heard that you can't rely on your carrier's breadown of data usage, because the time stamps are not always accurate. A data transfer shown at 5:00am might have taken place at any time that day... I don't know if I believe that, seems weird. Why even have it reported more than once a day then? Anyway...
So, even though I have nothing stored in iCloud (nothing AT ALL), I turned it off. While I watched the phone, it used 5 more MBs in a half hour.
So I uninstalled the Weather Channel. Then I turned off all location services except for the default weather widget, turned off automatic error reporting (Settings>General>About>Diagnostics & Usage), and turned off nearly all auto fetching and push notifications, especially those for facebook and my email.
Still kept racking up data while awake and on wifi. 100-200KB every few minutes, typically, versus my husband's 2KB over 2 hours.
So I uninstalled facebook. It seems to have helped. I've read a few posts that suggest that some apps use cellular data instead of wifi even when it's available. Maybe this is one of those.
I am also doing my best to remember to switch cellular data capability off at night (in settings). Would be GREAT if this could be turned on automatically.
So far, so good. But now I have a super duper expensive iPhone that is pretty much nothing more than a phone. I still have twitter on here but with no notifications enabled. I plan to wait a couple months and reinstall some of those other apps.
Amy and husband.