What is she called /nicknamed at the moment, I take it you are rejecting the old horseman's superstition about renaming horses being bad luck
?
I think nature-inspired names are nice for Welshies/little ponies, things like Holly, Rowan, Berry, Seren/Star, Luna, Fern, Sky, Willow, Robin, Poppy, Rose/Rosie, Lily? Or old-lady/milkmaid-ish names, I've known ponies called Polly, Molly, Dotty, Dora, Trudy, Queenie, Maggie, Bunty, Nellie, Bessie, Jenny, that kind of name?
Or along the Bounty/Coconut theme, maybe Polo, Minty, Candy, Snow(y), Alba (means white in Latin), Bianca (Bee for short?), Cloud, Daisy, Pearl? The only thing that would make me hesitate on choosing a too 'white' name would be if she's anything like most little ponies she'll be more of a fetching shade of green-brown most of the time!