No,not the little duns-one I saw was a palamino paint,the others had long white guard hairs with black points to blend in with the snow and rocks/branches...Don't know what color they would be when they shed off. There is a more comprehensive study on Wicopedia or "Ask" Siberain horses.
They also showed people riding reindeer!
The horses are called Yakut horses--come in bay,grey and dun.