Snow riding is all about technique. I ride in up to 6 inches of the white crap on a CX bike with no problems. You ARE going to go a lot slower in the snow. Don't hurry it, or you'll die. Here's knowledge I've grabbed from a few months of the icebike mailing list.
1. Use a lower gear. More work, but less spinouts.
2. Steer the bike under you rather than lean into turns.
3. Make sure you're using a winter grease. Shimano grease freezes easily. Snowmobile grease works well.
4. Clips, not clipless. Even platforms may work. Nashbar sells straps called powergrips that work well with boots.
5. Try an internally geared hub rather than single speeding it or a regular setup.
6. Keep clean. Very clean. You may need to wipe off and relube after every ride.
7. Keep your rims clean, check your brake pads often. Winter grime eats them away.
I replied to the other post, but theres some more things I guess I could elaborate on. Your bike is fine for winter riding. You're just not going to get much of anywhere in two feet of fresh snow. Your tires may even be really good for this weather -- if the snow isn't packed totally, all knobbies just turn into snow slicks after they pick some up off the ground.
Winter riding is a mix of technique and maintenance. I wouldn't go out and buy 3" tires and studded nokians yet, this isn't ice we're on, it's snow and that stuff doesn't do you a whole lot of good.
Just take it slow, and ride a whole lot. It's going to take a lot of practice. I ride a cross bike in this crap, and I do just fine. Just a lot slower than usual.