If you've ever taken a trip up into the mountains, you've likely noticed that it's cooler up there. That's because in the lower part of the atmosphere, the temperature drops as you go higher in altitude. On a rainy day in Seattle, the temperature drops roughly 2.5 degrees per 1,000 feet of altitude. That means when it's 40 degrees here in Seattle, it'll be in the low 30s in the mountain passes -- cold enough to snow.
Now, there's other factors involved in helping ski resorts pile up the snow -- sometimes colder air filters over the mountains from Eastern Washington. Also, strong downward winds from heavy showers can actually bring down colder air with them, dropping the temperature a few more degrees.