None of the major carriers including AT&T store any contents of your text messages, only dates, times and phone numbers involved online.  So rest assured none of your private stuff is online.  The Feds (NSA etc) do have the ability to see stuff as they are far more sophisticated.  They can read messages flying through the air lol (just kidding) they can plugin to the Tower itself to eavesdrop if they wanted to. can your wife or husband read your text online