While I agree it was private and you should have not read it I totally understand why you did. In fact I think I would have done the same thing (being totally honest here). We are put through hell and most likely don't even know the half of it. Lord knows we may never get the truth so I get why you looked. Right or wrong, I do understand.
I guess for me it would depend on what you read. Is it something you feel is a deal breaker for your marriage? If so then it is just time to move on. If it is not, then I think you need to wait to see if he tells you about it.