I went parasailing on our honeymoon in 2002 and horseback riding this past October.
I can comment a little on the parasailing.... let's just say that I didn't hate it, but I will never do it again! There were some breathtaking views, except I was too anxious to enjoy them. Although you are on a boat and flying over water, you do not get wet. You launch and land from a platform on the boat so no need for swimwear. We almost did not get to go because of the wind. If the wind is measured above a certain speed, it is not safe and they will not take you up. So keep in mind that even on a clear sunny day, you may not get to go. I went first when we went and I was hit by a few gusts and that was enough for me to determine that I did not need to do it again. When my husband went up after me, the guides on the boat said that they probably shouldn't have let him go up because the winds were at the maximum allowed when I went up. But since we hadn't gone back to check before it was his turn, they let him go too. He loved it! IIRC, you can choose from two different "heights". We were on the "platinum plan" (or whatever it was called) so we took the most expensive rides available. You can also do a tandem, but I think the weight limit essentially restricts it to an adult/child or child/child pairs. I can't recall the minimum age, but I know there was a 10 year old with us when we went.
As far as the horseback riding goes, it was an experience....nothing spectacular. It certainly wasn't exciting or thrilling. I can't really call it relaxing either since I was using muscles I didn't know I had to try and stay on the horse

. I would do it again, but I will wait until my kids are older and can go with me.