A snow demon is a very nasty creature that eats people, and can be very difficult to kill. It can apparently disguise itself as a human with white hair and icy eyes. It uses this disguise to get close to its victims. Once escape is impossible, it reveals its fangs and claws.
The Shin'a'in have a song ("Snow Beast") about a snow demon who ate half a clan before a kal'enedral finally killed it, and died doing so. The kal'enedral in question was one of Tarma's teachers, and claimed it was a very painful death. According to Tarma in Oathbreakers, this was during an unusually cold winter about four generations before. Given the time frame, it is likely the same creature Vanyel was referring to in Magic's Promise when he mentioned a Shin'a'in shaman coming to k'Treva for help with a creature that was destroying a clan.