: : : : There is a reference in Tolkien's appendices in LOTR.

: : : : There Helm Hammerhand is compared with a snow troll.

: : : Which doesn't prove that they existed: in our world, where trolls don't exist, story tellers made them up. In M-e. where they do, they could even more easily be used by story-tellers as an image of something terrible and implaccable, as Helm was as he sought his vengeance. The logic would be: Trolls exist, if there was a breed that was especially suited to harsh winters in the mountains, they'd be like King Helm was, so I'll describe Helm as a Snow Troll.

: : I think Snow Trolls (as well as Hill Trolls of the Ettenmoors, and possibly Stone-Giants) are the saem as Stone Trolls, but I'm really not sure.

: Are snow trolls the kind that, when you ask them if they are a troll, they say "snow"?

I couldn't tell you...I haven't really met any.