"I am a boy who went hiking recently with a female family friend around my age."
That's good, you're going out & doing things, not just texting; admirable. Spend time with God's daughters and take care of them, you'll make Him be a very happy Father.
"We went to a secluded lake she knew of to take a break and to eat some food. It was about ninety degrees, and we really wanted to cool off, so we decided to go swimming. She had a swimsuit, along with a few other supplies, that she permanently kept in a backpack that she used for hiking. I said I didn't have a swimsuit, so she asked me if I wanted to skinny dip."
This is a very big compliment; treat it as such, and don't let her down. If a girl feels safe enough to be stark naked around you, alone, that shows a vast amount of trust that very few people are seen as being worthy of. Please don't burn her, it's one of the most damaging things you can do to a girl.
"I said I would be uncomfortable with a naked girl."
I don't know the reasoning behind this decision, but if it's because you don't think you'd be able to control yourself, I applaud you greatly for knowing your strength. If it's because you're uncomfortable around any naked body, I highly advise you to look deep in your soul and see if you, as said in previous comments, automatically equate nakedness with sex. This will take much prayer, but nothing bad ever happened as a result of praying a lot.
"She said ok, if I thought I would be tempted that is ok."
Good, she's understanding; this could mean a few different things if she pushed you. Maybe it's just something she's used to, and doesn't understand why you wouldn't want to; maybe she would be the one wanting something sexual. Stay on high alert, anyone, if you're being pushed into a situation you don't like. Once again, prayer about it, prayer before anything happens that God will always guide you. "Draw near to God, and he will draw near to you." (James 4:8)
"So she asked me if just I wanted to skinny dip. She said she knew herself, and she wouldn't be uncomfortable or tempted."
Once again, know your strength. She knew she could handle it (though of course, less of a problem for a girl; men have twice as much brain matter dedicated to the sex drive, and are much more aroused by visuals).
"So I went skinny dipping and she swam in her bathing suit. Was that wrong?"
Overall, both of you handled the situation very well. A lot could've gone wrong, but nothing did. You have excellent self-control and insight; you went through the whole situation with good intentions, and that's perhaps the most important part. The human body is only sexual when we see it this way, it's certainly not created to be an object of lust. Remember, God created plants & declared them good; He created animals & declared them good; He created man and woman and declared them "VERY good". It's the devil that makes us have such a polluted view of ourselves. As a simple answer, no, I think you did nothing wrong, though do weigh the points that others have brought up, they have a lot of wisdom that we all could benefit from.
My only concern here, assuming there really were no sexual intentions, is the openness to the oppertunity to sin. But if, as it sounds like, you were both strong enough to tell Satan to stuff it, I don't think you did anything wrong. Walking through a store gives you the oppertunity to spend, but if your strong enough, it won't be a problem. The Catholic Church has a saint that spent every night for a significant portion of his life with prostitutes, but instead of using them, he brought them the Gospel, converting many of the & freeing them from their previous lives. Eventually, he was killed as he was walking out of a brothel, and following his funeral procession was an abundance of former prostitutes that followed him with candles and lanterns. Sometimes, being close to the oppertunity to sin can show the love & protection of God in a very powerful way. If nothing else, whether you know it or not, you made the girl feel much safer and happier about you and the world.
As far as private parts being "unpresentable", this may just be a reference to the culture of the time. There was no instruction given that "Do not show your genitalia to anyone but your spouse", as such instructions are commonly given in Paul's letters; simply a reference to these parts being "unpresentable" may just be how they were seen by Paul and the people he was around. Do keep in mind that the purpose of this entire passage is showing the importance of every part of the body of Christ, not a lesson in Jesus-based dress code. I don't know if my interpretation here is right or not, please do correct me if you think it needs changed, I want to be a professor of theology one day so these lessons would be much appreciated, and thank you all for the excellent discussion throughout the comments.
I highly advise everyone to look up Jason Evert on YouTube; he has an abundance of excellent talks on various points of Theology of the Body. He's also written several excellent books on the subject (available on Amazon, of course; I most recomment the Theology of His/Her Body flip book, it literally changed my life & deepened my spirituality farther than I thought possible).