I'm sorry to say this is a big deal, and it can lead to an bigger deal if nothing is done. You listened to your gut feeling, you felt uneasy for a reason and your instincts were right. If he was texting another woman, telling her lies and making plans for them to 'hang out'.. this sounds like a man that's already in or waiting to get himself into deep trouble.

You already don't trust him now, because after reading those text messages I can only imagine the amount distrust you feel towards him. And you have all the rights to feel this way, you have to point this out to him. It being indirectly or direct, but let him know there is something wrong and ask him everything now is the time to clear everything out. If you don't want to point it out just yet or need more 'proof' of what's going on without asking, you can keep snooping. (But, don't wait too long..)

I don't know the type of man he is, there are people who would just admit it and then there are those who would run around the bush until you forgive them. "She's just a friend, why are you snooping on me to begin with?, I can't have girl friends now?" and the list goes on. Be prepared for any of those response, and do what makes you feel right. He has to be open with you and not lie or talking to other women in that way behind your back, especially if this is someone whose planning on asking you to marry him in the future. These type of things setback accomplishments in a relationship, if you do decide to forgive him then that's a whole process of trusting again. I understand he treats you well, and no one is perfect but if he continues to do this behind your back, I'm sure you're already aware of what it can lead to.

Hope you're able to find some comfort through all this!