I don't know what kind of email your ex uses, but I was not aware that there was a way to tell when the account was last logged into. What makes you know this to be a fact? (I'm no pro, but have never heard of this)
Because you have been in a serious relationship with your new boyfriend for a year, and the fact that this has upset you so much, I would be inclined to tell him. If it was in fact, a one time stupid drunken thing, done on the spur of the moment, he might think it was a weird thing to do, but, there was no harm done- it was just a mistake in judgment on your part.
But, should you confess after the fact, he might automatically think that if you do these things behind his back, what else have you done. Checked his email? Gone through his cell phone? I think that he will also most likely consider you to be a sneaky person, and trust would come into play- if this all comes to light through him simply finding out, and not from you.
I don't know what motivated you to snoop in your ex boyfriends email account; he should have changed his password a year ago just to avoid the possibility of this happening.