I don't think you did anything wrong at all. That other mother should definitely have been watching her 3yr old (in the POOL no less!!). No, she should have been IN the pool with her daughter. And it was her responsibility to remove the noodle AND graciously give it back to you. That was just rude of her.
That being said, with my first kid, I was all about "let's share with other kids at the pool/park, etc". By the time my third kid came along, I learned that some parents are kinda picky, so I would glance over at them and ask "is it ok if your child plays with this?" before handing them the item.
It's sort of along the same lines as sharing a cracker or cookie. The *nice* thing, obviously, is to offer the treat to the 3yr old child who is staring at your own child devouring the cookie. But I would be pretty upset if someone gave my child a cookie without checking with me first. I know, not the exact same issue, and I can't imagine NOT keeping eagle-eyes on my 3yr old kid in a pool at all times, but maybe from now on, just a quick check in with the parent would ease your mind about handing over something that *seems* harmless. And please don't stop sharing, *most* parents LOVE it when cool stuff shows up at the pool and their child is given the chance to play with it.