My Cunning 3 Year Old....

It's good to teach her that was wrong.
However, instead of telling her directly I like to walk my daughter through the issue until she comes to that conclusion herself. (Do you think it was fair to the other kids you got an extra cookie? How would you feel if someone lied to you? What do you think you should do next time...? Etc.)
She might be a little young to completely get it, but I believe helping them think through the issues will help them in the long run.
That's how I try to handle these types of issues.
:)

The only thing that comes to my mind is come dinner time your 3 year old may not quite get it why she is being punished for something that happened hours ago. I agree she already had enough dessert. I don't think you blew her openness with you. If it was my child I may have just only talked to her then like you did and just not brought up dessert for dinner.
What a smart little one you have!

Wow to her openness with you! That is so wonderful. Her sneakiness wasn't so cool and being direct is very good...but I agree with others. Maybe taking her through the scenario till she sees what was wrong on her own would be good. With holding dessert, I feel, was a good thing since she did have some already, but you could have done that after she went through it with you - something like well since you know that was wrong we can't do dessert b/c you already had so much. It is good to set her straight otherwise it becomes a habit. However, having her come to the conclusion of wrong is important too because then she understands why it was wrong and will work through other situations the same way. At least it seems that she has a conscious already! FOr her to admit that shows a girl who can see something was wrong and bravo to you for raising a girl like that! I would have laughed later at her admittedly blunt honesty!! Too good.

I think being direct as you were is the way to go. A 3 yo is trying out things in her world to see what happens and you reacted in an honest way letting her know that sneakiness and lies are not the right things to do.

As to not giving her desert, I agree that she might not make the connection. If you told her after dinner why she wasn't getting the dessert she knows the connection.

Perhaps you did this but I'd add to praise her for telling you the truth. The message you are giving is that there are consequences for sneaking an extra cookie has a consequence. Telling you the truth is rewarded by praise. Not having dessert is a natural consequence.

I think you did the right thing.

The thing I would have done different is not punish her by withholding dessert. She was honest with you and she sees very smart to have done the maneuver.I wouldn't want to jeopardize future openness with her. She's young enough that she probually will be open in the future too.

I agree with everything said already here, but the only thing that I would add is that it might be a good idea to talk to her again and point out that she knew it was wrong when she did it, because she had to hide it from the teacher and talked about being afraid that she would get caught. Talking her through those feelings and pointing out what they mean might be another way to go.