There was this really old anime, but I don't think it was a series. There were many movies though. It had many whimsical fantasy themes such as magical forests. It was called the Adventures of Unico and was about a little unicorn who could grant wishes. It was a very kid oriented movie, and so there is a good possibility of a young child watching it. The art style you mentioned is the only thing that reminded me of it. You said they had small chins etc. and I immediately thought of art styles from the 80's like Leiji Matsumoto's Harlock or Galaxy Express 999. This was a typical style for beautiful people in the early days of anime when shows like Galaxy 999 and Robotech were prominent.
Here are some links to images
Were the main characters human or animal?