Snow is rather hap-hazard and rare in Seattle - so let it dump on your monitor (plus, its a simple effect to give your artistic creation a little je-ne-sais-quoi).
There are many ways to make it snow in your Flash creations. For those of us who are somewhat code challenged - here is the quick-and-dirty without a line of actionscript (well, maybe one). I've been using this for some time now - works great for rain, flower petals, monkey heads...you got the idea.
STEP1: Create an empty movie clip in your library. Add a snowflake graphic (which you can create to your heart's desire) and attach it to a squiggly guide running from the top of your scene to the bottom and motion-tween it (this emulates Earth's gravitational pull). You can give your snowflake some rotation as it drifts in the wind - do this by highlighting your 1st frame and selecting a rotation direction and number of rotations in your parameters menu. Now, feel free to create your own weather effects - the shallower the guide slope and the closer the gap between the start and end frame the more blizzard-like your snowfall will become - makes sense.
STEP2: Create yet another empty movie clip in your library. Drag and drop a few of your snowflake clips onto the stage. So that they don't all start at once, place each on a different frame on your timeline. Since each is its own movie clip, you may want to insert a "stop" action onto your final frame on the timeline.
STEP3: Back to your original scene. From the library drag and drop as may of your STEP2 movie clips onto the stage (again, have them on different frames). Now save and publish your movie, sit back and enjoy the snow.
As you may guess - the above can also be accomplished relying heavily on actionscript. I've tried this myself, and it works just as well - I just find that there are too many areas to slip-up when coding is not a natural talent. In a nutshell, you start with your snow flake graphic, convert it into a movie clip, add some "math functions", "physical parameters" and "if / else clauses", and plug in your numbers. Now drag and drop just one flake outside your scene and add some more actionscript to its frame - creating a final touch of randomness - resulting in a more realistic weather effect once saved and published!