The Rainbow Curl Ponies were the second set of ponies to feature ringlet hair, giving some logic to their names. According to UK ponylore they lived in Rainbow Mountain, and I remember very distinctly that Rainbow Magic was the granter of wishes...the reason I recall this so strongly is that I had her new as a child and that was the reason I chose her.
Hasbro in America gave these pretty little ponies shorter names which were easier to remember but somehow stripped them of their magic - Rainbow Magic was 'Ringlet', Rainbow Rider, 'Streaky', Rainbow Storyteller 'Stripes' and Rainbow Cloud 'Raincurl'. Like with the Candy Canes, it's hard to find these four with mint ringlets, though the ponies themselves are not htf.
It's probably important to note that Rainbow Magic does not have a symbol per se like the others - she has rainbow coloured wings and little stars and dots leading from the tops of her front legs to her wings in 3 coloured sprays. Sadly the hair kinda got in the way in my picture, but you can just about see her wing tips :)