Hmmm, first off, if you’re smart, don’t take my advice. My results in the field of relationships speak for themselves 
Having warned you: There are several foundational issues to a good relationship: True- genuine love, mutual respect, trust, friendship and a dose of passion.
Now, snooping was (IMO) wrong. You got, unfortunately, what you get when you snoop. Had you not found something it is likely you would not have stopped snooping, perhaps you would have continued until you did find something.
This part is not her issue, it is yours. Perhaps what she did is wrong, perhaps not. But one thing for sure, there is only one person who’s behavior you can influence: Yours.
Additonally it kind of indicates the level of trust you guys have. Maybe not so good. Have you asked yourself why you didn’t just say, “Um, was there something going on I might want to know about, or you would want to know about if I did the same thing to you?”
I guess the best thing to do may be to discuss the issue honestly and openly and see what develops from there. Perhaps the key here is to get all the cards on the table- her’s and yours. Try to listen as best you can. that;s hard when you’re upset.
If she is important to you think about her response. Also, think about your response. It’s a difficult situation. I’ve been in similar and was not able to resolve it, and we both tried pretty hard for a while, but probably at different times. Then it just ended badly.
I do wish you luck. Consider how you want your life to look and how you want hers to look. Remember that true love is selfless, trusting and giving- especially when things are rocky.
There are few things in this world I believe in, but I know the power of love is the most powerful force in human nature.
Good luck my friend.