Looking at the ponies in my current fort, there seems to be no pattern across castes. Each caste has it's colour scheme defined individually to create variety, and this is the current state of them, on the 14th Slate, Mid-Spring, 1004, with 77 cave ponies:
Male Draltha Pony: moss green hair, rust coat, consistently.
Female Draltha Pony: lemon hair, coats can be heliotrope, red, cobalt, aqua, lilac, midnight blue, peach, pumpkin, azure.
Male Slippy Pony: teal and pearl striped hair, coats can be azure, red, black, crimson(occurs twice), brown, emerald, auburn, flax.
Female Slippy Pony: buff and goldenrod striped hair, buff coat.
Male Gorlak Pony: carmine hair with crimson spots, dark violet coat.
Female Gorlak Pony: dark blue, dark violet and pale chetsnut striped hair, coat can be dark olive, rust, dark indigo, dark chestnut, ivory, aqua.
Male Underlord Pony(only two): violet hair, chartreuse or dark brown coat.
Female Underlord Pony(only one): cobalt, amethyst and fuchshia striped hair, pine green coat.
No discernible pattern in coat or hair colour, though there isn't a skin colour defined. It's interesting how coat colour is either dominated by one colour or seemingly random. I also wouldn't expect new migrants to have the same coat and hair colour as members of the initial group if the environment were affecting them.
Anyway, easy way to test this in your worlds: note down which civ your dorfs are from, abandon the fort, settle a completely different biome with the same civ and check skin and hair colour.