I think the issue is whether this was a drunken one off or an indication of something else................ I would wonder if continuing with texts after the event does not suggest a one of drunken event .............and the fact that he didn't delete the texts ( which any subtle philanderer would do ) , makes me wonder if he wanted you to find the texts..................
I think you know he has erred deliberately...............he wants you to confront him, he wants you to know.........................believe me, if he did it and didn't want you to know he would have done that and nothing would have changed for you because you wouldn't have known.
The important thing is how you deal with this now..........and denial is not necessarily a good idea.........although understandably a comfortable one !!
Good luck