Ice and snow - - no, but you'll be soaking wet.

The Pacific Coast has a Mediterranean climate with a very significant precipitation maximum in Dec/Jan. Aberdeen, Washington gets 13 inches of rain in January. Average high/low - 46/35 - not exactly pleasant cycling weather. Reedsport, Oregon gets 13 inches of rain in January, too, but drops to 9 1/2 in February. It drops to 8 1/2 inches for Crescent City, California in March. Even Santa Cruz gets 4 1/3 inches of rain in March.

There's a reason nearly everybody does the Pacific Coast in summer.

http://www.wrcc.dri.edu/precip.html
Click on the months in the right-hand column to see percentages of precipitation each month in the West.
I think the Southern Tier is much more appropriate. Maybe run the border from Boca Chica, Texas to Tijuana, Baja California.