Possible, yes. Whether it's advisable depends on a lot of things.
Spokane's snow removal procedure consists basically of letting cars pack the snow into a sheet of ice and then blowing de-icer all over it until it melts. Trails don't get plowed, and bike lanes will be completely unusable if there's any accumulation at all. Arterials will be a rutty, slushy, sloppy, crappy mess for the most part.
I commuted daily through last winter, but I ride down Howard from the North Side, which is relatively flat, low-traffic and has lots of room for error. There were times when the downtown streets were so rutted with ice that I just walked instead.
If you're just riding occasionlly/recreationally, I'd make sure you've got something with knobbies and head out on the side streets right after the snow falls. There are few things that beat rolling through fresh powder at night.
Also, keep an eye on the FBC blog and this site for group rides throughout the winter. We had a lot of fun last year despite (or perhaps because of) the conditions. Huevos Rancheros, anyone?