Not much of Snowpaw's past is revealed, but she died when Howlpaw accidentaly dislodged a boulder that killed her when they were hunting. StarClan thinks that Howlpaw did this on purpose, making him end up in the Dark Forest, but it was truly an accident.
When Snowpaw was alive, she had a crush on Howlpaw. She still likes him even in StarClan. Snowpaw was overjoyed when Cardinalblaze brought Howlpaw to StarClan.