Depending on what part of the Pac NW you mean, the influence of La Niña on precipitation can be pretty strong. You can look back at these maps to see the patterns during 20 of the strongest La Niñas on record. That's total precip, though, not distinguishing rain from snow. Sometime before winter, we will probably do a La Niña version of this post, so stay tuned. You also have to keep in mind that long-term global warming is reducing snowfall in many U.S. locations; a percentage of winter precip that would have historically fallen as snow now falls as rain. So, it's possible that even if La Niña did historically tend to produce snowier winters in a particular place, it's impact may be more muted in today's warming climate. (Sorry to be a downer, if you are a snow fan!)